Non-gauge forces
Dr Tim
What would such a force be like?
Hendrik van Hees
> Are there any non-gauge forces?
> What would such a force be like?
The standard model of elementary particles is a gauge theory, based on th=
e
local gauge group SU(3) x SU(2) x U(1) (colour SU(3), weak isospin SU(2),
weak hypercharge U(1)).
The only interaction terms, which are not due to the minimal coupling to =
the
corresponding gauge boson fields (i.e., the gluon, weakon and photon
fields), are the Yukawa-couplings of the leptons and quarks to the Higgs
boson and the Higgs self-interactions, necessary to give the leptons and
the weakons their masses in accordance with the principle of local gauge
invariance. This together with the freedom of the model from anomalies (o=
f
the local gauge symmetry, not of the accidental symmetries which can be
anomalously broken, e.g., the U_A(1)-Anomaly which is important for the
correct rate of neutral pion decays!) ensures the renormalisability and
unitarity of the standard model.=20
--=20
Hendrik van Hees Fakult=E4t f=FCr Physik=20
Phone: +49 521/106-6221 Universit=E4t Bielefeld=20
Fax: +49 521/106-2961 Universit=E4tsstra=DFe 25=20
http://theory.gsi.de/~vanhees/ D-33615 Bielefeld=20
Dr Tim
That's a bit beyond my current understanding!
But you seem to be saying that
the Higgs mechanism is not a gauge theory.
Is that correct?
A.J. Tolland
On Mon, 18 Aug 2003, Dr Tim wrote:
> Are there any non-gauge forces?
The Higgs particles can mediate interactions in much the same way
as the gauge bosons. That is to say, there are diagrams of two particles
passing in the night and exchanging a Higgs boson. The Higgs is quite
massive however, so don't expect it to give a very impressive force.
I should mention that the Higgs particle has not been discovered,
so it might not qualify as a "known non-gauge force" depending on how
strict one feels. Most particle physicists suspect it is real... Our
models don't work at all well without it.
One could also make a (somewhat semantic) argument that gravity is
not a gauge force. Gravity does seem to have quite a lot in common with
gauge field, in that it requires something like gauge invariance to work.
> What would such a force be like?
None of the examples I know of are terribly different from the
gauge fields.
--A.J.
A.J. Tolland
Yes. The Higgs mechanism is a trick for giving mass to gauge
fields. It uses a set of particles called the Higgs particles.
I'm a tiny bit rusty, but I don't believe that anyone would call
the theory describing the Higgs particle itself a gauge theory. It _is_
coupled to a gauge theory, which muddies the waters a little. The point
is that there are certain redundancies built into the description of
states built with gauge fields.
This is a bit of a semantic quibble. The Higgs mechanism is only
used in gauge theories, so there are always gauge symmetries present when
you're talking about the Higgs. But they act trivially on the Higgs
particle.
--A.J.
Hendrik van Hees
Dr Tim wrote:
> But you seem to be saying that
> the Higgs mechanism is not a gauge theory.
> Is that correct?
The Higgs mechanism is impossible without gauge theory. It is the
spontaneous breaking of a local gauge symmetry.
Spontaneous breaking of a symmetry means that the equations of motion
are symmetric under certain transformations of its consituents
(coordinates in mechanics or fields), i.e., they do not change under
these transformations.
In field theory there are two general types of symmetries, global and
local ones. In the case of global symmetries the symmetry
transformations are independent of the space-time variables. The most
simple symmetry of this kind is phase symmetry of (complex) fields. For
instance, the most general renormalisable phase symmetric Lagrangian
for a free complex scalar field reads
L=(\partial_\mu phi)^*(\partial^{\mu} \phi) - m^2 |phi|^2 -la/8 |phi|^4
It is invariant under the transformation
phi(x)->exp(i alpha) phi(x)
phi^*(x) -> exp(-i alpha) phi(x)
From Noether's theorem we know that there exists a conserved current due
to that symmetry.
Now suppose we give m^2 a negative sign. Then phi=0 is not a stable
state any more but there is a minimum in the potential at a circle
|phi|=phi_0 in field space. Due to phase symmetry each phi with
|phi|=phi0 is a possible stable vacuum with the same energy then and
there is no cost of energy to change from one vacuum state to the
other. This means, there exists a massless field mode. On the other
hand to change phi such that |phi| becomes different from |phi_0| costs
energy and thus we have also a massive particle in the game.
No each vacuum with phi_0\neq 0 is not symmetric under the phase
transformations, but the equations of motion are. This is what is meant
by the term spontaneous symmetry breaking. Our heuristic argument above
has shown that the spontaneous symmetry breaking gives the existence of
a massless particle. This can be generalised to more complicated cases
of symmetries and field contents: Each spontaneously broken
(continuous) global symmetry yields another masselss bosonic mode. This
is known as the Nambu-Goldstone bosons.
The physics changes when the theory is "gauged". This means one tries to
make the Lagrangian symmetric under local gauge transformations, i.e.,
one tries to construct a Lagrangian which is symmetric under the
symmetry transformations, but where the phase alpha can be space-time
dependent, i.e., an arbitrary scalar field rather than a constant. The
original Lagrangian is not symmetric under such transformations but it
can be made symmetric by introduction of a vector field. Then one
writes instead of the partial derivatives
\partial_{\mu} -> D_{\mu} = \partial_{\mu} - i e A_{\mu}
Then the Lagrangian is symmetric under the local transformations
phi(x) -> exp(i e chi(x)) phi(x)
phi^*(x)->exp(-i e chi(x)) phi(x)
A_{\mu}(x) -> A_{\mu}(x) + \partial_{\mu} chi(x)
Here e is an arbitrary real constant, the gauge coupling constant.
Now we only need a kinetic term for the gauge field A_{\mu}, which is
given in terms of the "Faraday tensor"
F_{\mu \nu}=\partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}
L_{0A}=-1/4 F_{\mu \nu} F^{\mu \nu}
As one can easily see by inspection of the equations of motion, the
gauge field is massless if the scalar mass m^2>0.
Now, again we make m^2<0. Again the new vacuum for the scalar field is
some phi with |phi|=phi_0. Then we can write the scalar field as
phi(x)=exp[i e chi(x)] [phi_0+phi'(x)]
Then in the Lagrangian the chi(x) never appears explicitly since the
Lagrangian is invariant under *local* gauge transformations, but the
gauge fields gets a mass term \propto phi_0^2. Thus, the chi(x)-field
degree has not simply vanished by magic but "eaten up" by the gauge
field, because, since the vector field is massive now, it has three
physical field degrees of freedom instead of two in the massless case.
As we have seen on this most simple example (the Abelian Higgs model),
if a local gauge symmetry is broken, the Goldstone theorem is not valid
any more: There is *no* massless Nambu-Goldstone boson but the
corresponding field degrees of freedom (in our case the phase chi(x))
are used to give the third component for a massive vector field. The
vector field, corresponding to the spontaneously broken symmetry
becomes massive.
Also this idea can be generalised to more complicated local gauge
theories, like the standard model of electro-weak interactions, where
the SU(2) x U(1) local gauge symmetry is spontaneously broken to U(1),
i.e., of the four gauge fields the 3 corresponding to the SU(2) become
massive (these are the W- and Z-bosons of the standard model) and one
remains massless (the photon in the standard model).
NB: All these classical arguments survive quantisation, provided the
local gauge symmetry has no anomalies (if a local gauge theory is
anomalously broken, the theory becomes physically senseless).
--
Hendrik van Hees Fakultät für Physik
Phone: +49 521/106-6221 Universität Bielefeld
Fax: +49 521/106-2961 Universitätsstraße 25
http://theory.gsi.de/~vanhees/ D-33615 Bielefeld
Mike Mowbray
"A.J. Tolland" wrote:
> [...] The Higgs mechanism is only used in gauge theories,
> so there are always gauge symmetries present when you're
> talking about the Higgs. But they act trivially on the
> Higgs particle.
Umm, what exactly did you mean by "[gauge symmetries] act
trivially on the Higgs particle"? The Higgs field in the
usual Standard Model transforms as a *doublet* under
SU(2)L, doesn't it?
- MikeM.
John Baez
Dr Tim <timro...@paradise.net.nz> wrote, failing to properly
cite a post by someone he refers to as "you":
>But you seem to be saying that
>the Higgs mechanism is not a gauge theory.
>Is that correct?
The Higgs mechanism is not a gauge theory; it's
something that happens in certain gauge theories,
which lets gauge bosons become massive. Before
it was discovered, everyone thought gauge bosons
had to be massless, so nobody knew how to explain
the weak force using gauge theory. The weak force,
being short-ranged, needs a massive particle to
carry it.
For a good nontechnical book on particle physics, try this:
Robert P. Crease and Charles C. Mann, The Second Creation:
Makers of the Revolution in Twentieth-Century Physics,
MacMillan, New York, 1986.
It doesn't go into much detail, but it gives a good
overview of the history and a decent introduction to
some of the jargon.
John Baez
Hendrik van Hees <he...@physik.uni-bielefeld.de> wrote:
>A.J. Tolland wrote:
>> One could also make a (somewhat semantic) argument that gravity is
>> not a gauge force. Gravity does seem to have quite a lot in common
>> with gauge field, in that it requires something like gauge invariance
>> to work.
>From my point of view, Einstein's GRT *is* a gauge theory, where the
>local gauge group is that of local diffeomorphisms of space time, i.e.
>a local GL(4).
Well, people say lots of things like this, but it's a bit weird to
equate "local diffeomorphisms" with "GL(4) gauge transformations".
The diffeomorphism group is just not a group of gauge transformations
in the standard sense of "bundle automorphisms that act as the
identity on the base space". If you're trying to argue that gravity
is a gauge theory, the best you can do (in my opinion) is to point
out that you can formulate it using an SO(3,1) connection together
with a cotetrad field - and then you can lump both of these together
into a Poincare group connection. It's still quite different from,
say, a Yang-Mills theory.
the softrat
On Thu, 28 Aug 2003 08:17:19 +0000 (UTC), Hendrik van Hees
<he...@physik.uni-bielefeld.de> wrote:
>
>From my point of view, Einstein's GRT *is* a gauge theory, where the
>local gauge group is that of local diffeomorphisms of space time, i.e.
>a local GL(4).
>
>group is not compact.
>
I just know that I have to do a lot more study when I realize that the
only technical words in the above that I think I understand are
'group' and 'spacetime'. And I hold a Master of Science degree in
Physics!
GRT, gauge theory, local gauge group, diffeomorphism, local, GL(4),
Yang-Mills gauge theory, compact
GRT : ? General Relativity ?
GL(4) : ? some kind of group, probably continuous ?
George D. Freeman IV
the softrat ==> Careful!
I have a hug and I know how to use it!
mailto:sof...@pobox.com
--
"Will the two hobbits please climb out of the balrog costume?!"
-- Peter Jackson (alleged)
A.J. Tolland
Yes, you're absolutely right.
I was thinking of something else rather closely related. I should
have been far more careful about how I expressed this.
My point of view is somewhat idiosyncratic; I'm not at all sure
that most folks would agree with my thinking here. That said, I would
argue that what we normally call the group of gauge symmetries does not
act on the Higgs particle as a gauge symmetry. The idea here is that when
we take the BRST cohomology to construct our Hilbert space, the gauge
fields lose 2 degrees of freedom per gauge symmetry. The scalar fields do
not. Likewise, the spinor fields.
Simple example: U(1) gauge field coupled to a single complex
scalar field. Naive degrees of freedom: 2 scalar, 4 vector. Actual
count: 2 scalar, 2 vector. You might want to argue that what I really
have is 1 scalar, 3 vector. I'm happier keeping different kinds of
degrees of freedom separated.
I think that the term gauge symmetry ought to be reserved for
those symmetries which cut down the naive number of degrees of freedom.
A gauge transformation does something interesting to a gauge field. It
basically just rephases everything else.
So yes, I'm a heretic. Or at least something of a weirdo when it
comes to the Higgs mechanism. I don't mind admitting that there's an
effective low energy theory involving a massive field and a real scalar.
I just don't like viewing the fundamental theory in those terms.
Sorry about the sloppiness the first time. Does I make sense
now?
--A.J.
Starblade Darksquall
ba...@galaxy.ucr.edu (John Baez) wrote in message news:<birki9$dpm$1...@glue.ucr.edu>...
> In article <7fed4c14.03082...@posting.google.com>,
> Dr Tim <timro...@paradise.net.nz> wrote, failing to properly
> cite a post by someone he refers to as "you":
>
> >But you seem to be saying that
> >the Higgs mechanism is not a gauge theory.
> >Is that correct?
>
> The Higgs mechanism is not a gauge theory; it's
> something that happens in certain gauge theories,
> which lets gauge bosons become massive. Before
> it was discovered, everyone thought gauge bosons
> had to be massless, so nobody knew how to explain
> the weak force using gauge theory. The weak force,
> being short-ranged, needs a massive particle to
> carry it.
>
Well, if there are only 3 weak gauge bosons, then they don't HAVE to
be massive in order for the force to be short ranged. Think about the
color force, and how it has 8 carrier type bosons, which I guess are
gauge bosons but they're not called that, they're called gluons. If
you can have color confinement then you can also have massles gauge
bosons which are short range through a similar process.
Of course, we've already shown which masses they have, and that they
DO have masses, so it's not really necessary anyways.
(...Starblade Riven Darksquall...)
[Moderator's note: The strong force is not short-ranged. It is
precisely because it acts strongly at a distance that confinement
occurs.
-- KS]
Dr Tim
ba...@galaxy.ucr.edu (John Baez), who is very particular about citations,
>
> Robert P. Crease and Charles C. Mann, The Second Creation:
> Makers of the Revolution in Twentieth-Century Physics,
> MacMillan, New York, 1986.
>
> It doesn't go into much detail, but it gives a good
> overview of the history and a decent introduction to
> some of the jargon.
Does this include any equations?
I'm sick of books leaving out the intesting stuff
just because it involves mathematics.
Because of nontechnical books,
I know nothing useful about the weak force.
Nontechnical books draw Feynman diagrams but don't
give any details about calculating them,
nor the equation they are supposed to approximate.
Grrr!
Mike Mowbray
>>> [...] The Higgs mechanism is only used in gauge
>>> theories so there are always gauge symmetries present
>>> when you're talking about the Higgs. But they act
>>> trivially on the Higgs particle.
I wrote:
>> Umm, what exactly did you mean by "[gauge symmetries]
>> act trivially on the Higgs particle"? The Higgs field
>> in the usual Standard Model transforms as a *doublet*
>> under SU(2)L, doesn't it?
A.J. Tolland wrote:
> Yes, you're absolutely right. I was thinking of something
> else rather closely related. I should have been far more
> careful about how I expressed this.
>
> My point of view is somewhat idiosyncratic; [...] I would
> argue that what we normally call the group of gauge
> symmetries does not act on the Higgs particle as a gauge
> symmetry.
(Hmmm.... definitely not in Kansas any more...)
> The idea here is that when we take the BRST cohomology
> to construct our Hilbert space, the gauge fields lose
> 2 degrees of freedom per gauge symmetry. The scalar
> fields do not. Likewise, the spinor fields.
I'm not as fluent in BRST techniques as I probably should be.
It's basically a way of handling constraints, e.g: the
mass-shell condition, right?
> Simple example: U(1) gauge field coupled to a single
> complex scalar field.
OK... electromagnetism coupled to a charged scalar field...
> Naive degrees of freedom: 2 scalar, 4 vector.
> Actual count: 2 scalar, 2 vector.
I had always believed this was due to the masslessness of
the photon, and Wigner's theory of Poincare' irreps,
i.e: massless vector irreps only have 2 degrees of freedom.
(Or is this just a different, less sophisticated, way of
saying what you already said?)
> You might want to argue that what I really have is
> 1 scalar, 3 vector. [...]
No, I'm happy enough with 2+2.
> I think that the term gauge symmetry ought to be
> reserved for those symmetries which cut down the naive
> number of degrees of freedom. A gauge transformation
> does something interesting to a gauge field.
> It basically just rephases everything else.
But such rephasings are detectable via Aharonov-Bohm
effects, aren't they? Such effects certainly count as
"interesting" imho. (Well, ok, it's actually rephasing
*differences* that are detectable, if you want to split
hairs. :-)
> So yes, I'm a heretic. Or at least something of a weirdo
> when it comes to the Higgs mechanism. I don't mind
> admitting that there's an effective low energy theory
> involving a massive field and a real scalar. I just don't
> like viewing the fundamental theory in those terms.
Well, I'd like first to understand your point of view
more thoroughly before I form an opinion whether it's
"weird", or just "different". :-)
> Sorry about the sloppiness the first time.
> Do I make sense now?
Not entirely, but that might be due to my lack of fluency
with BRST techniques. IIUC, you're saying that instead of
writing "... [gauge symmetries] act trivially on the Higgs
particle", you should probably have written something like:
"...[gauge symmetries] do not reduce the degrees of freedom
of the Higgs particle".(?)
- MikeM.
John Baez
Dr Tim <timro...@paradise.net.nz> wrote:
>ba...@galaxy.ucr.edu (John Baez) wrote:
>> For a good nontechnical book on particle physics, try this:
>>
>> Robert P. Crease and Charles C. Mann, The Second Creation:
>> Makers of the Revolution in Twentieth-Century Physics,
>> MacMillan, New York, 1986.
>>
>> It doesn't go into much detail, but it gives a good
>> overview of the history and a decent introduction to
>> some of the jargon.
>Does this include any equations?
No. Since you asked if the Higgs mechanism was
a gauge theory, it seemed that what you needed was
not so much equations as a good general overview
of particle physics. And, since particle physics
is best tackled by first learning a bit of its history
(from electrons, protons and neutrons all the way
to the Standard Model), I offered a nice history
of the subject.
>I'm sick of books leaving out the intesting stuff
>just because it involves mathematics.
Okay. If you want a historical introduction to
particle physics with more math, try this:
Abraham Pais, Inward Bound: of Matter and Forces
in the Physical World, Clarendon Press, New York, 1986.
>Because of nontechnical books,
>I know nothing useful about the weak force.
Both the above books are very good, not just
pop fluff. Everyone who likes particle physics
should read them! But if you actually want to
learn the details of particle physics, I'd suggest
reading these *too*:
T. D. Lee, Particle Physics and Introduction to Field Theory,
Harwood, 1981.
Kerson Huang, Quarks, Leptons & Gauge Fields, World Scientific,
1982.
The second one has a particularly nice explanation of the Higgs
mechanism. To fully appreciate this stuff you'll need some
books on quantum field theory, too. Assuming you have the
prerequisites (namely quantum mechanics, electromagnetism
and special relativity) I suggest starting with this:
Michael E. Peskin and Daniel V. Schroeder, An Introduction to
Quantum Field Theory, Addison-Wesley, 1995.
If you're particularly interested in the weak interaction,
this book is great:
K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear,
Particle, and Astrophysics, Hilger, Bristol, 1990.
.....................................................................
I replaced the headlights on my car with strobe lights. Now it looks
like I'm the only one moving. - Steven Wright
Lubos Motl
> Simple example: U(1) gauge field coupled to a single complex
> scalar field. Naive degrees of freedom: 2 scalar, 4 vector. Actual
> count: 2 scalar, 2 vector. You might want to argue that what I really
> have is 1 scalar, 3 vector. I'm happier keeping different kinds of
> degrees of freedom separated.
You might be happier, but the rest of us who "believe" that a vector is
something different than a scalar ;-) can only be happy with one answer.
If you define your theory and your vacuum well-enough, only of the answers
can be correct!
If the gauge symmetry is not spontaneously broken - like in QED - then it
is only the vector gauge field, as you said correctly, that loses 2
degrees of freedom because of the gauge symmetry. By the way, "losing the
degrees of freedom" is something different than "transforming under the
gauge symmetry". The electron's Dirac field does not lose any degrees of
freedom, but it still transforms under the gauge symmetry!
Let me return to the counting of vector and scalar degrees of freedom.
For example, 4 components of the electromagnetic potential in QED are
reduced to 2 physical polarizations (x,y, for example): the 2 killed
components contain one that is pure gauge (and hence unphysical) and the
second one that is killed by the Gauss' law constraint. No components of
scalar or fermionic fields are removed by the gauge symmetry. A complex
scalar field in a U(1) theory will continue to have 2 real polarizations.
The situation is different if you have a background with the Higgs
mechanism. In that case, the gauge field - or at least some components of
the gauge field (by component, I now mean a different adjoint index of the
gauge group) become massive - for example the W+, W-, and Z bosons in the
electroweak theory. Massive vector fields in 3 spatial dimensions just
can't have 2 polarizations only because the physical polarizations must
transform as a spin 1 representation of the SO(3) rotational symmetry!
Clearly, the massive gauge field has 3 polarizations, not 2, and an
explicit calculation of the Higgs mechanism confirms this claim. However,
the total number of degrees of freedom is unchanged. If we return to the
example of a U(1) gauge theory with a complex scalar field, then: the
complex scalar field originally had 2 real polarizations, but after the
spontaneous symmetry breaking takes place, it has 1 real polarization
only! This real polarization corresponds to the fluctuations in the radial
direction of the "Mexican hat" potential. The other component of the
scalar field - that corresponds to the fluctuations around the
circumference of the minimum in the Mexican hat potential - is "eaten" by
the gauge field.
So before you break the symmetry, you have 2 states coming from the
(massless) vector gauge field, and 2 real states coming from the scalar.
The Higgs mechanism causes that the gauge field "eats" a component of the
scalar, so you end up with 3 polarizations of the (massive) gauge field,
and 1 real polarization of the scalar!
> I think that the term gauge symmetry ought to be reserved for
> those symmetries which cut down the naive number of degrees of freedom.
So far so good.
> A gauge transformation does something interesting to a gauge field. It
> basically just rephases everything else.
But if it rephases "something else", then it implies that "something else"
IS transforming under the gauge symmetry. If the symmetry remains
unbroken, it is only the gauge field that loses the degrees of freedom.
But it is enough to show that it was a gauge symmetry. However other
fields DO transform under the symmetry as well. They are not losing
degrees of freedom, but they DO transform under the gauge symmetry because
they change their phases.
Moreover, if the symmetry is broken by the Higgs mechanism, then the gauge
field and a scalar field share the lost degrees of freedom: each of them
loses one degree of freedom, as explained above. I hope that now you will
have enough data to understand the simple error that you are doing all the
time. You seem to underestimate the importance of the "rephasing". If you
have a complex number and you "rephase" it so that it becomes real and
positive, you *do* kill a degree of freedom - namely the phase - much like
you can kill it by the transformation law for the vector gauge field. The
vector gauge field and the scalars transforms differently, but both of
them transform and - in the case of the broken symmetry - both of them are
losing a degree of freedom!
> So yes, I'm a heretic. Or at least something of a weirdo when it
> comes to the Higgs mechanism. I don't mind admitting that there's an
> effective low energy theory involving a massive field and a real scalar.
> I just don't like viewing the fundamental theory in those terms.
You can use any terms to describe a theory with the broken symmetry. For
example, you can work in the unitary gauge where you directly expand
physics around the spontaneously broken point of the configuration space.
What we call "gauge symmetry" will have a lot of consequences for your
attempts to construct a meaningful action. A textbook constructing the
electroweak theory in this way was written by J. Horejsi
http://www.amazon.com/exec/obidos/tg/detail/-/9810218575
Finally, you will succeed. But you will miss a lot of beauty and
understanding if you completely avoid the "alternative", "pretty"
formulation of the electroweak theory that has a gauge symmetry to start
with, and this symmetry is broken by the Higgs mechanism.
> Sorry about the sloppiness the first time. Does I make sense now?
No, it did not, but I hope that it will make a bit more sense now.
Best wishes
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
phone: work: +1-617/496-8199 home: +1-617/868-4487
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Superstring/M-theory is the language in which God wrote the world.
Starblade Darksquall
news:<4aa861fb.03083...@posting.google.com>...
[wads of unnecessary quoted text deleted by grumpy moderator]
> [Moderator's note: The strong force is not short-ranged. It is
> precisely because it acts strongly at a distance that confinement
> occurs. -- KS]
Well apparantly I was wrong about the whole strong force thing... I
originally thought it had something to do with the number of gauge
bosons, and the fact that it is a SU (Special Unitary) group rather
than just a U (Unitary) group. It was described to me this way.
Apparantly whoever described it this way wasn't being clear.
However, I wonder what would happen with virtual strong-force type
particles, such as quarks or gluons, or the virtual fields that exist
in free space. Wouldn't they REALLY disrupt matter, or do they just
stop existing, or cancel each other out at some point?
Furthermore, does the strong force go to infinity at infinite range...
and does it do so slowly, quickly, or in between, or does it
eventually converge to a single strength?
(...Starblade Riven Darksquall...)
Lubos Motl
> [Moderator's note: The strong force is not short-ranged. It is
> precisely because it acts strongly at a distance that confinement
> occurs. -- KS]
Well, the strong force between two charged objects - e.g. quarks with some
color - does not even decrease to zero as the distance goes to infinity.
In this sense the strong force is not short-ranged. However the same
feature of this force implies confinement, i.e. that only color-neutral
objects such as the proton can exist as isolated entities.
The force between two neutrons is a manifestation of the same strong
force, and the force between two neutrons simply *is* short-ranged; it
only exists in the vicinity of the nucleus. This is how the strong force
was understood before the quarks were found, and therefore the strong
force *is* counted as a short-ranged force, see for example
http://zebu.uoregon.edu/~soper/Sun/particles.html
Today it looks even more reasonable to consider the strong force to be
short-ranged because we know that the Higgs mechanism and the confinement
can be dual (equivalent, although not obviously) manifestations of the
same effect. Because the Higgs mechanism causes the forces (at least a
part of them) to be short-ranged, it then follows that confinement is able
to do the same job.
Kevin A. Scaldeferri
<Pine.LNX.4.31.030904...@lamb.physics.harvard.edu>,
Lubos Motl <mo...@feynman.harvard.edu> wrote:
>> [Moderator's note: The strong force is not short-ranged. It is
>> precisely because it acts strongly at a distance that confinement
>> occurs. -- KS]
>Well, the strong force between two charged objects - e.g. quarks with some
>color - does not even decrease to zero as the distance goes to infinity.
>In this sense the strong force is not short-ranged. However the same
>feature of this force implies confinement, i.e. that only color-neutral
>objects such as the proton can exist as isolated entities.
>
>The force between two neutrons is a manifestation of the same strong
>force, and the force between two neutrons simply *is* short-ranged; it
>only exists in the vicinity of the nucleus. This is how the strong force
>was understood before the quarks were found, and therefore the strong
>force *is* counted as a short-ranged force, see for example
>
> http://zebu.uoregon.edu/~soper/Sun/particles.html
I think we both can agree that such popular depictions should not be
considered authoritative.
This view that the "residual strong force" is short-ranged therefore
the strong force is short-ranged seem to me analogous to trying to
claim that EM is short-ranged because van der Waals forces are.
>Today it looks even more reasonable to consider the strong force to be
>short-ranged because we know that the Higgs mechanism and the confinement
>can be dual (equivalent, although not obviously) manifestations of the
>same effect. Because the Higgs mechanism causes the forces (at least a
>part of them) to be short-ranged, it then follows that confinement is able
>to do the same job.
Hmm... perhaps this is true in some stringy or SUSY Yang-Mills theory,
however I wouldn't depend on it for "real" Yang-Mills. If you could
prove it, though (and put confinement on a rigorous basis), I think
there is a big check waiting for you.
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
Kevin A. Scaldeferri
In article <4aa861fb.03090...@posting.google.com>,
Starblade Darksquall <Starb...@Yahoo.com> wrote:
>Starb...@Yahoo.com (Starblade Darksquall) wrote in message
>news:<4aa861fb.03083...@posting.google.com>...
>> [Moderator's note: The strong force is not short-ranged. It is
>> precisely because it acts strongly at a distance that confinement
>> occurs. -- KS]
>Well apparantly I was wrong about the whole strong force thing... I
>originally thought it had something to do with the number of gauge
>bosons, and the fact that it is a SU (Special Unitary) group rather
>than just a U (Unitary) group. It was described to me this way.
>Apparantly whoever described it this way wasn't being clear.
No, that's definitely not the case. Maybe you or they were getting
confused with asymptotic freedom, which is related to the size of the
gauge group (and which is generally believe to imply confinement,
although this is not proven).
>Furthermore, does the strong force go to infinity at infinite range...
>and does it do so slowly, quickly, or in between, or does it
>eventually converge to a single strength?
So much as one can actually talk about forces and potentials in the
context of QFT, the force between color-charges particles is more or
less constant beyond a certain seperation. Alternatively, you can say
that there is a linearly increasing term in the potential.
Starblade Darksquall
> >originally thought it had something to do with the number of gauge
> >bosons, and the fact that it is a SU (Special Unitary) group rather
> >than just a U (Unitary) group. It was described to me this way.
> >Apparantly whoever described it this way wasn't being clear.
>
> No, that's definitely not the case. Maybe you or they were getting
> confused with asymptotic freedom, which is related to the size of the
> gauge group (and which is generally believe to imply confinement,
> although this is not proven).
>
Yeah, somebody told me color confinement would only work if there were
8 gluons. But if you say it has to do with the size of the gauge
group, then tell me this: Why is the weak force weaker than the
electromagnetic force? It has a larger gauge group, after all.
Or, better yet, if the weak force were carried by massless vector
bosons, how would the weak force change?
> >Furthermore, does the strong force go to infinity at infinite range...
> >and does it do so slowly, quickly, or in between, or does it
> >eventually converge to a single strength?
>
> So much as one can actually talk about forces and potentials in the
> context of QFT, the force between color-charges particles is more or
> less constant beyond a certain seperation. Alternatively, you can say
> that there is a linearly increasing term in the potential.
Well if the term is linearly increasing, does this mean that the color
force grows linearly with distance, or that it levels out?
I think what's also confusing the issue is that the color force does
not ACT linearly. It does not follow the superposition principle like
the electromagnetic force does. I am now at the point where I can
understand what this means. This essentially means that you can't just
add two color fields together to get the correct result when
calculating the color force.
I already know what happens to quarks, but an explaination of the
effects on the color field and the gluons would help. For example, if
a gluon were 'emitted' straight 'up' (out) from a baryon, what is
keeping it from going on forever and just losing a lot of energy but
not quite stopping?
(...Starblade Riven Darksquall...)
Kevin A. Scaldeferri
Starblade Darksquall <Starb...@Yahoo.com> wrote:
> Some poor soul not cited by Kevin Scaldeferri wrote:
>> Some other poor soul not cited by Kevin Scaldeferri wrote:
>> >Well apparantly I was wrong about the whole strong force thing... I
>> >originally thought it had something to do with the number of gauge
>> >bosons, and the fact that it is a SU (Special Unitary) group rather
>> >than just a U (Unitary) group. It was described to me this way.
>> >Apparantly whoever described it this way wasn't being clear.
>> No, that's definitely not the case. Maybe you or they were getting
>> confused with asymptotic freedom, which is related to the size of the
>> gauge group (and which is generally believe to imply confinement,
>> although this is not proven).
>Yeah, somebody told me color confinement would only work if there were
>8 gluons. But if you say it has to do with the size of the gauge
>group, then tell me this: Why is the weak force weaker than the
>electromagnetic force? It has a larger gauge group, after all.
Neither EM nor the weak force are confining in the sense that we
normally use that word.
The weak force is weak because the gauge bosons are very massive, not
because of the size of the coupling constant.
>> >Furthermore, does the strong force go to infinity at infinite range...
>> >and does it do so slowly, quickly, or in between, or does it
>> >eventually converge to a single strength?
>> So much as one can actually talk about forces and potentials in the
>> context of QFT, the force between color-charges particles is more or
>> less constant beyond a certain seperation. Alternatively, you can say
>> that there is a linearly increasing term in the potential.
>Well if the term is linearly increasing, does this mean that the color
>force grows linearly with distance, or that it levels out?
Force equals derivative of potential. Linearly increasing potential
means constant force.
>I already know what happens to quarks, but an explaination of the
>effects on the color field and the gluons would help. For example, if
>a gluon were 'emitted' straight 'up' (out) from a baryon, what is
>keeping it from going on forever and just losing a lot of energy but
>not quite stopping?
Same thing as a quark (at the level of detail we're discussing). It
loses a constant amount of energy for each femtometer it travels. It
does not get very far.
Jeffery
> In article <4aa861fb.03090...@posting.google.com>,
> Starblade Darksquall <Starb...@Yahoo.com> wrote:
>
> >Starb...@Yahoo.com (Starblade Darksquall) wrote in message
> >news:<4aa861fb.03083...@posting.google.com>...
>
> >> [Moderator's note: The strong force is not short-ranged. It is
> >> precisely because it acts strongly at a distance that confinement
> >> occurs. -- KS]
>
> >Well apparantly I was wrong about the whole strong force thing... I
> >originally thought it had something to do with the number of gauge
> >bosons, and the fact that it is a SU (Special Unitary) group rather
> >than just a U (Unitary) group. It was described to me this way.
> >Apparantly whoever described it this way wasn't being clear.
>
> No, that's definitely not the case. Maybe you or they were getting
> confused with asymptotic freedom, which is related to the size of the
> gauge group (and which is generally believe to imply confinement,
> although this is not proven).
>
> >Furthermore, does the strong force go to infinity at infinite range...
> >and does it do so slowly, quickly, or in between, or does it
> >eventually converge to a single strength?
>
> So much as one can actually talk about forces and potentials in the
> context of QFT, the force between color-charges particles is more or
> less constant beyond a certain seperation. Alternatively, you can say
> that there is a linearly increasing term in the potential.
This is not true. The strong force is short range because of
confinement. The weak force is short range because the Higgs mechanism
gives masses to the W and Z bosons. The strong force and weak force
are short range forces. Electromagnetism and gravity are long range
forces. This is why the strong force and weak force were not known
before the 20th century. It is the SU(3) gauge group of the strong
force that is the reason why you have colored gluons, which are what
causes confinement, which is what causes the strong force to be a
short range force. Therefore the fact that the strong force is short
range is due to the SU(3) gauge group.
Jeffery Winkler
Kevin A. Scaldeferri
In article <325dbaf1.03091...@posting.google.com>,
Jeffery <jeffery...@mail.com> wrote:
>ke...@its.caltech.edu (Kevin A. Scaldeferri) wrote in message
news:<bjldmi$48p$1...@clyde.its.caltech.edu>...
>> In article <4aa861fb.03090...@posting.google.com>,
>> Starblade Darksquall <Starb...@Yahoo.com> wrote:
>> >Furthermore, does the strong force go to infinity at infinite range...
>> >and does it do so slowly, quickly, or in between, or does it
>> >eventually converge to a single strength?
>> So much as one can actually talk about forces and potentials in the
>> context of QFT, the force between color-charges particles is more or
>> less constant beyond a certain separation. Alternatively, you can say
>> that there is a linearly increasing term in the potential.
>This is not true.
You disagree that the potential is linearly rising?
> The strong force is short range because of confinement.
I don't know if you have seen my response to Lubos Motl on this issue,
specificially the analogy to van der Waals forces. I'm not going to
repeat it here, so if you disagree you should respond to is there.
> The weak force is short range because the Higgs mechanism
>gives masses to the W and Z bosons. The strong force and weak force
>are short range forces. Electromagnetism and gravity are long range
>forces.
Let us consider a thought experiment. Imagine that through some means
you produced a quark and an oppositely colored anti-quark separated by
a distance some orders of magnitude greater than a fermi and further
seperated from the rest of the universe. What do you believe would
happen? I.e. what force would the quarks experience or what would the
energy of this configuration be? How would it depend on the
separation distance?
In my opinion of what short-ranged and long-ranged mean, if you think
that the strong force is short-ranged then the answers must be that
there is no force to speak of and that the energy doesn't depend on
the separation. (More precisely, they are exponentially small.) On
the other hand, if you think that the quarks experience an attractive
force or that the energy depends polynomially on the distance, then
you must conclude that the strong force is long-ranged.
colone...@yahoo.com
>
> In article <325dbaf1.03091...@posting.google.com>,
> Jeffery <jeffery...@mail.com> wrote:
>
> >ke...@its.caltech.edu (Kevin A. Scaldeferri) wrote in message
in color neutral configurations, so at long ranges the effect of the
color force cancels. So the range of the color force is short"
Unfortunately, this is not the standard meaning of a short ranged force in
particle physics. Maybe if you said "strong force is -effectively- short
ranged" people would be happier.
Also, some older texts where the strong force == the nuclear force,
it is referred to as "short ranged". That description is disappreciated.
> > The weak force is short range because the Higgs mechanism
> >gives masses to the W and Z bosons. The strong force and weak force
> >are short range forces. Electromagnetism and gravity are long range
> >forces.
But in the sense above, the gravitional force has a longer -effective-
range than E&M because it isn't screened.
> Let us consider a thought experiment. Imagine that through some means
> you produced a quark and an oppositely colored anti-quark separated by
> a distance some orders of magnitude greater than a fermi and further
> seperated from the rest of the universe. What do you believe would
> happen? I.e. what force would the quarks experience or what would the
> energy of this configuration be? How would it depend on the
> separation distance?
The quarks would move toward each other to put a bat out of the forsaken
regions to shame, through a mess of pair-produces quarks, anti-quarks
and other crud at first. But after a few fermi/c they'd have lost
interest in each other and be happily co-habating with (a) younger**
quark(s). :p
3ch
"It would take a trained mathematician a month, working night and
day, to dig a hole that can be dug by a modern backhoe in one hour."
Lubos Motl
> You disagree that the potential is linearly rising?
Do you think that the potential at long distances is guaranteed to be
exactly linear, even without logarithmic corrections? Moreover, does
this question make sense? The long "string" between the quark and the
antiquark in the real QCD is very unstable anyway.
> I don't know if you have seen my response to Lubos Motl on this issue,
> specificially the analogy to van der Waals forces. I'm not going to
> repeat it here, so if you disagree you should respond to is there.
It is a good analogy to compare the van der Waals forces with the
(short-range) forces between nucleons that can be explained by an
exchange of pions. However the comparison of the strong force between
quarks with the electrostatic force between charged particles is not
so appropriate because the electrically charged particles can exist in
isolation while the color-charged particles can't.
It is not legitimate to consider electrically neutral particles only -
because the charged particles can be pair-produced. However, it is
totally legitimate - for the purpose of low-energy effective
description - to consider the color-neutral objects only - these are
the only ones than can exist in isolation. Then it is correct to say
that the strong force is a short-range force, and this is what is
usually done.
> >The weak force is short range because the Higgs mechanism
> >gives masses to the W and Z bosons. The strong force and weak force
> >are short range forces. Electromagnetism and gravity are long range
> >forces.
This is the usual categorization.
> Let us consider a thought experiment. Imagine that through some means
> you produced a quark and an oppositely colored anti-quark separated by
> a distance some orders of magnitude greater than a fermi and further
> seperated from the rest of the universe.
The physical laws don't allow you to create the quarks without the
appropriate non-Abelian fields, and the Yang-Mills fields always imply
that separated quarks always carry a large positive potential
energy. I am not precisely sure which state in the Hilbert space you
want to call "quark plus antiquark separated by one meter", but what I
*am* sure is that any attempt to take the description "quark plus
antiquark separated by one meter" seriously will lead to
contradictions. The reason is simple: the confinement is a *real*
phenomenon and every statement that pretends that you can ignore it is
an illusion.
There is no state in the Hilbert space that contains a quark and an
antiquark separated by 1 meter and whose energy is smaller than 10^10
GeV.
Quarks can be never separated from one another and from the rest of
the Universe. You can say that it is "just" because the potential
energy would be virtually infinite, but the choice of your
justification does not really matter. Quarks can only be considered as
isolated objects at distances of order 1 fermi or shorter where they
enjoy asymptotic freedom. I am not saying that long-distance
processes can't be described by QCD; but I am saying that quarks
should not be viewed as physical objects at macroscopic length scales.
> What do you believe would happen? I.e. what force would the quarks
> experience or what would the energy of this configuration be? How
> would it depend on the separation distance?
This is a question about a non-existing (and internally inconsistent)
Universe - because of the reasons above - and therefore no one needs
to answer this question. You can define your inconsistent Universe in
any way you want, but it will still be inconsistent. ;-)
> In my opinion of what short-ranged and long-ranged mean, if you think
> that the strong force is short-ranged then the answers must be that
> there is no force to speak of and that the energy doesn't depend on
> the separation. (More precisely, they are exponentially small.)
It does not have to be exponential. Van der Waals forces don't
decrease exponentially - rather as the exotic power laws - but they
are still short-ranged forces. A decrease faster than 1/r (in the
potential) is OK. The strong force is also a short-range force in the
sense that it decreases as a power law between physical
(color-neutral) objects.
> On the other hand, if you think that the quarks experience an
> attractive force or that the energy depends polynomially on the
> distance, then you must conclude that the strong force is long-ranged.
Isolated quarks are wrong degrees of freedom for describing long
distances, and therefore you can't conclude anything.
A confined force should be also thought of as a short-range force
because confinement and the Higgs mechanism - that obviously gives
short-range forces - can be dual to one another in various situations.
Best wishes
Lubos
Jeffery
> In article <325dbaf1.03091...@posting.google.com>,
> Jeffery <jeffery...@mail.com> wrote:
>
> >ke...@its.caltech.edu (Kevin A. Scaldeferri) wrote in message
> news:<bjldmi$48p$1...@clyde.its.caltech.edu>...
>
> >> In article <4aa861fb.03090...@posting.google.com>,
> >> Starblade Darksquall <Starb...@Yahoo.com> wrote:
>
> >> >Furthermore, does the strong force go to infinity at infinite range...
> >> >and does it do so slowly, quickly, or in between, or does it
> >> >eventually converge to a single strength?
>
> >> So much as one can actually talk about forces and potentials in the
> >> context of QFT, the force between color-charges particles is more or
> >> less constant beyond a certain separation. Alternatively, you can say
> >> that there is a linearly increasing term in the potential.
>
> >This is not true.
>
> You disagree that the potential is linearly rising?
No, I do not
>
> > The strong force is short range because of confinement.
>
> I don't know if you have seen my response to Lubos Motl on this issue,
> specificially the analogy to van der Waals forces. I'm not going to
> repeat it here, so if you disagree you should respond to is there.
I think the strong force analog of van der Waals forces would be the
residual strong force felt between nucleons that binds them together
into the nucleus.
>
> > The weak force is short range because the Higgs mechanism
> >gives masses to the W and Z bosons. The strong force and weak force
> >are short range forces. Electromagnetism and gravity are long range
> >forces.
>
> Let us consider a thought experiment. Imagine that through some means
> you produced a quark and an oppositely colored anti-quark separated by
> a distance some orders of magnitude greater than a fermi and further
> seperated from the rest of the universe. What do you believe would
> happen? I.e. what force would the quarks experience or what would the
> energy of this configuration be? How would it depend on the
> separation distance?
>
> In my opinion of what short-ranged and long-ranged mean, if you think
> that the strong force is short-ranged then the answers must be that
> there is no force to speak of and that the energy doesn't depend on
> the separation. (More precisely, they are exponentially small.) On
> the other hand, if you think that the quarks experience an attractive
> force or that the energy depends polynomially on the distance, then
> you must conclude that the strong force is long-ranged.
In your hypothetical example, yes there would be a strong force
between the two quarks. If you could magically create two quarks a
light year apart, they would feel a strong between. If that's what you
mean by long range, then I agree it's long range. The point I'm making
is that that hypothetical would never happen in reality. You can never
get two quarks far apart. If you try to pull a hadron apart, the color
tube between the quarks contains enough energy to create new
particles, which it then does, which is what creates the hadron jets
in particle accelerators. Therefore you can never get two quarks far
apart. Therefore you can never get the strong force to exert its
affects over the long distances. The strong force is not felt over
distances of about a fermi, due to confinement. This is why most
people say the strong force is a short range force, because we don't
detect it over long distances.
Jeffery Winkler
Zig
Jeffery wrote:
>
> In your hypothetical example, yes there would be a strong force
> between the two quarks. If you could magically create two quarks a
> light year apart, they would feel a strong between. If that's what you
> mean by long range, then I agree it's long range. The point I'm making
> is that that hypothetical would never happen in reality. You can never
> get two quarks far apart.
in the early universe, weren t there supposedly lots of free quarks,
when the temperature was high enough? would it make sense in that
context to talk about the force between quarks with large seperation?
Jeffery
Zig <jha...@wisc.REMOVEME.edu> wrote in message news:<bkjas3$s1q$1...@news.doit.wisc.edu>...
Yes, that's true. In that case, it would be.
Jeffery Winkler