Quark Quantum # Conservation?
Steve Harris
Uncle Al wrote in message <3B391C12...@hate.spam.net>...
>Are quark flavor and color conserved quantities?
Color can't be, since quarks attempting to be free just draw anticolored
quarks out of the vacuum to clothe themselves up as new hadrons, and nobody,
not
God or anybody, seems to care.
As for flavor, I think that flavor conservation in the form of electron
number,
muon number, etc, was added to the standard model by hand. Neutrino
oscillation, more or less now observed at SNO and long suspected from
the solar neutrino problem, pretty much killed it as a Law. It seems to be
conserved in a lot of ordinary reactions though (muon neutrinos don't act
like
electron neutrinos in observed events), so the reason why it's approximately
conserved, remains a mystery.
Overall non-conservation of lepton number was pretty much assumed in the
Black Holes Have No Hair theorem, from which where Hawking evaporation
of black holes (black holes aren't so black) was implicitly assumed to
depend only on the Hole's mass, charge, and angular
momentum, and not on its baryon number or lepton number(s).
Thus the Harris' Lollipop Corollary:
Black Holes Suck So Much They've Lost All Flavor.
SBH
George Jones
> Uncle Al wrote in message <3B391C12...@hate.spam.net>...
> >Are quark flavor and color conserved quantities?
>
> Color can't be, since quarks attempting to be free just draw anticolored
> quarks out of the vacuum to clothe themselves up as new hadrons, and nobody,
> not
> God or anybody, seems to care.
Quark-antiquark pairs are "produced", so colour content is left unaltered.
> As for flavor, I think that flavor conservation in the form of electron
> number,
> muon number, etc, was added to the standard model by hand. Neutrino
> oscillation, more or less now observed at SNO and long suspected from
> the solar neutrino problem, pretty much killed it as a Law. It seems to be
> conserved in a lot of ordinary reactions though (muon neutrinos don't act
> like
> electron neutrinos in observed events), so the reason why it's approximately
> conserved, remains a mystery.
>
> Overall non-conservation of lepton number was pretty much assumed in the
> Black Holes Have No Hair theorem, from which where Hawking evaporation
> of black holes (black holes aren't so black) was implicitly assumed to
> depend only on the Hole's mass, charge, and angular
> momentum, and not on its baryon number or lepton number(s).
>
> Thus the Harris' Lollipop Corollary:
>
> Black Holes Suck So Much They've Lost All Flavor.
Yes, Blacks Hole Have No Hair is quite interesting. I wonder how it
will play out in a quantum theory of gravity.
Regards,
George
Matthew Nobes
>
> Uncle Al wrote in message <3B391C12...@hate.spam.net>...
> >Are quark flavor and color conserved quantities?
Colour yes, flavour no. Weak interactions can mix quark
flavours, the CKM matrix parametrizes this.
> Color can't be, since quarks attempting to be free just draw
> anticolored quarks out of the vacuum to clothe themselves up
> as new hadrons, and nobody, not God or anybody, seems to
> care.
Huh? The reaction that produced said quark must have created an
anti-quark at the same time. Subsquent q\bar{q} pairs will
always conserve colour.
[snip rest, I'm sure Uncle Al can do it justice]
--
"Neutral kaons are even more crazy than silly putty"
-G. 't Hooft
Matthew Nobes, c/o Physics Dept. Simon Fraser University, 8888 University
Drive Burnaby, B.C., Canada, http://www.sfu.ca/~manobes
Uncle Al
>
> On Tue, 26 Jun 2001, Steve Harris wrote:
>
> >
> > Uncle Al wrote in message <3B391C12...@hate.spam.net>...
> > >Are quark flavor and color conserved quantities?
>
> Colour yes, flavour no. Weak interactions can mix quark
> flavours, the CKM matrix parametrizes this.
>
> > Color can't be, since quarks attempting to be free just draw
> > anticolored quarks out of the vacuum to clothe themselves up
> > as new hadrons, and nobody, not God or anybody, seems to
> > care.
>
> Huh? The reaction that produced said quark must have created an
> anti-quark at the same time. Subsquent q\bar{q} pairs will
> always conserve colour.
>
> [snip rest, I'm sure Uncle Al can do it justice]
(Uncle Al can ID the Shinola.)
Is this OK with everybody?
http://www.mazepath.com/uncleal/gravtable.htm
If anyone can name the missing invariances that bring forth the
last seven conserved quantities, you get citations. I was
debating replacing "Conserved Quantity" with "Charge Current,"
but does that make it any clearer?
--
Uncle Al
http://www.mazepath.com/uncleal/
http://www.ultra.net.au/~wisby/uncleal/
(Toxic URLs! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Matthew Nobes
> Matthew Nobes wrote:
> >
> > On Tue, 26 Jun 2001, Steve Harris wrote:
> >
> > >
> > > Uncle Al wrote in message <3B391C12...@hate.spam.net>...
> > > >Are quark flavor and color conserved quantities?
> >
> > Colour yes, flavour no. Weak interactions can mix quark
> > flavours, the CKM matrix parametrizes this.
> >
> > > Color can't be, since quarks attempting to be free just draw
> > > anticolored quarks out of the vacuum to clothe themselves up
> > > as new hadrons, and nobody, not God or anybody, seems to
> > > care.
> >
> > Huh? The reaction that produced said quark must have created an
> > anti-quark at the same time. Subsquent q\bar{q} pairs will
> > always conserve colour.
> >
> > [snip rest, I'm sure Uncle Al can do it justice]
>
> (Uncle Al can ID the Shinola.)
>
> Is this OK with everybody?
> http://www.mazepath.com/uncleal/gravtable.htm
>
> If anyone can name the missing invariances that bring forth the
> last seven conserved quantities, you get citations. I was
> debating replacing "Conserved Quantity" with "Charge Current,"
> but does that make it any clearer?
Well quark colour comes from the internal (unbroken) SU(3).
Quark flavour is not conserved. Baryon number is a consquence of
a global U(1). IIRC, it is exactly conserved in the standard
model.
I can't remember if the neutrino ocillations now mean that lepton
number can be violated, my guess is that it can. The symmetry
that provides the conservation eludes me at the moment (it's
probably U(1) though).
Isospin is an approximate SU(2) symmetry of QCD. The
approximation is exact when the masses of the up and down are
both zero. But in the real world, it's not conserved.
As for your usage ```conserved quantity'' is what I'd use.
One other thing, there are two ``types'' of both Isospin and
hypercharge. The more common is the usage in terms of hadronic
physics, but sometimes you'll see the SU(2) of the electroweak
interactions refered to as ``weak isospin'' and the U(1) of the
electroweak interaction refered to as ``weak hypercharge''.
A good treatment of these things can be found in Kerson Huang's
book ``Quarks, Leptons and Gauge Fields''
Jim Heckman
On 27-Jun-2001, Matthew Nobes <man...@fraser.sfu.ca> wrote:
[...]
> Well quark colour comes from the internal (unbroken) SU(3).
> Quark flavour is not conserved. Baryon number is a consquence of
> a global U(1). IIRC, it is exactly conserved in the standard
> model.
Could you say a little bit more about how this global U(1) for baryon
number arises from U(1)xSU(2)xSU(3)?
--
Jim Heckman
George Jones
George Jones
Sorry for the blank reply. I'm just learning a little about this myself,
and I intended to build a reply as I learned. I hit Send by mistake. I
wanted to wait until Matthew Nobes, someone who actually knows about
QCD and the standard model, replied. I didn't know about global U(1)
until I read his post yesterday.
Now that the damage has been done, I'll say what little I've learned.
The global (i.e., ungauged) U(1) symmetry is related to gauged
U(1)xSU(2)xSU(3) symmetry in a somewhat indirect way.
6 quark flavours, 2 chiralities, and 3 colours results in an initial
U(36) global symmetry for the kinetic term. This U(36) does not act on
the gauge bosons, so a subgroup of U(36) that commutes with
U(1)xSU(2)xSU(3) is needed. Consistency with things like quark charges
requires this subgroup to be U(3)^3. The Higgs mechanism breaks the
global U(3)^3 down to a global U(1) symmetry that gives rise to baryon
conservation.
Regards,
George
Gordon D. Pusch
> 6 quark flavours, 2 chiralities, and 3 colours results in an initial
> U(36) global symmetry for the kinetic term. This U(36) does not act on
> the gauge bosons, so a subgroup of U(36) that commutes with
> U(1)xSU(2)xSU(3) is needed. Consistency with things like quark charges
> requires this subgroup to be U(3)^3. The Higgs mechanism breaks the
> global U(3)^3 down to a global U(1) symmetry that gives rise to baryon
> conservation.
It should be noted that the actual conserved quantity in the Standard Model
is not B, but rather (B-L). E.g., a proton can still decay to a positron
in the Standard Model (via an ``instanton'' mediated process); however,
the mean lifetime for this mode is absurdly long --- something like
10^120 years, IIRC...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Jim Heckman
Where did you learn all this in one day?! Is there a good book that talks
about this kind of stuff?
--
Jim Heckman
George Jones
> Is there a good book that talks about this kind of stuff?
The more I look at it, the more I like the book "Quantum Field Theory
for Mathematicians" by Robin Ticciati, though at $110, it isn't cheap.
I don't like the title. In my opinion, this is a physics book, not a
math book, and the title is enough to put many physicists off. I think,
given the right instructor, this book could (should?) be used for
standard physics grad courses in field theory.
If you do a Google search for "Ticciati" on sci.physics.research,
you'll find a thread where I asked people on spr their opinion of this
book. The response was favourable.
In my previous post, I just repeated what's in this book, but I hope I
have some understanding of what I wrote.
Regards,
George
Matthew Nobes
> Jim Heckman wrote:
>
> > Is there a good book that talks about this kind of stuff?
>
> The more I look at it, the more I like the book "Quantum Field Theory
> for Mathematicians" by Robin Ticciati, though at $110, it isn't cheap.
>
> I don't like the title. In my opinion, this is a physics book, not a
> math book, and the title is enough to put many physicists off. I think,
> given the right instructor, this book could (should?) be used for
> standard physics grad courses in field theory.
I'll second that recomendation. A fellow grad student in my
office has had it out of the library for many months running now,
and it sees a fair amount of use.
But you don't need that much power for this. Like I said to
Uncle Al, Kerson Huang's ``Quark's Leptons and Gauge Fields''
covers this. You could also (probably) get some of this out of
``Group Structure of Gague Theories'' by L. O'Raifeartaigh.
Or maybe Georgi's book (Lie Algebras in Particle Physics IIRC).
> If you do a Google search for "Ticciati" on sci.physics.research,
> you'll find a thread where I asked people on spr their opinion of this
> book. The response was favourable.
>
> In my previous post, I just repeated what's in this book, but I hope I
> have some understanding of what I wrote.
Does everybody undertand how the global U(1) gives conservation
of Baryon number? (or more correctly B-L) I could post that, if
there's interest.
Y.Porat
i think that never in the history of modern scince
(i do not speak about the theological ages)
were so many moutains of empty garbage talking was done
with so little experimental backing behind it
as in the 'quark story'
just remember what old Catto saied:
the main body of the nucleid, includes no quarks
and no shmarks!
i must add in favour of you fellows, that lately
i see more and more question marks (?)
in your texts
ie some wake up is going on about it
people start to feel that it has been too long that they
were pulled too much at their noses
all the best
Y.Porat
Matthew Nobes <man...@fraser.sfu.ca> wrote in message news:<Pine.GSO.4.30.010629...@fraser.sfu.ca>...
Mark William Hopkins
>Are quark flavor and color conserved quantities?
Color is conserved.
The Weak Nuclear Force violates particle flavor and just about everything
else. Except color, charge and isospin.
>Color can't be...
Asking the question is the same thing as saying you don't know the
answer.
me...@cars3.uchicago.edu
There is nothing wrong with not knowing the answer, as long as you're
willing to ask the question and to listen to the answers you get.
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Mark William Hopkins
>> Baryon number is a consquence of a global U(1). IIRC, it is exactly
>> conserved in the standard model.
>
>Could you say a little bit more about how this global U(1) for baryon
>number arises from U(1)xSU(2)xSU(3)?
It doesn't, and it can't come from there or any extension of U(2)xSU(3).
It's a global symmetry and not a local symmetry.
(Footnote: U(1)xSU(2) = U(2)).
Aside from the 4 quantum numbers contained in U(2)xSU(3), the only
other (generation-independent) quantum number that can arise from a local
symmetry is the
Red + Green + Blue - 3*Lepton
number (or, basically: the Baryon - Lepton number).
Baryon number conservation doesn't come from anywhere and is probably
false since the net baryon number is a gezillion -- probably evenly
matched by the net lepton number, which raises a strong suspicion that
something exists which can convert between baryons and anti-leptons;
and between leptons and anti-baryons. Something which can only occur
at superhigh temperature can convert between positrons and protons;
electrons and anti-protons. Hotter even than the inside of a supernova.
So the baryon number assymmetry is primordal going all the way back to
some unimaginable inferno that took place at the beginning of time.
Mark William Hopkins
>It should be noted that the actual conserved quantity in the Standard Model
>is not B, but rather (B-L). E.g., a proton can still decay to a positron
>in the Standard Model (via an ``instanton'' mediated process); however,
>the mean lifetime for this mode is absurdly long --- something like
>10^120 years, IIRC...
B and L are both converved in the Standard Model. There are no
proton decays in the Standard Model. Proton decays are features of
the so-called GUT's which try to go beyond the Standard Model.
That's half the reason it's called "Standard Model". The name was
intended as a cynical tongue-in-cheek term. And that's why there are
a zillion books out there called "The Standard Model AND BEYOND".
Mark William Hopkins
>Jim Heckman wrote:
>
>> Is there a good book that talks about this kind of stuff?
>
>The more I look at it, the more I like the book "Quantum Field Theory
>for Mathematicians" by Robin Ticciati, though at $110, it isn't cheap.
But its whole take on the so-called infinities and divergences is totally
misleading.
You can do perturbation theory, without divergences of any kind, and
without the need for renormalization by simply handling the mathematics
of distributions in the correct fashion (particularly, by defining the
time ordered product correctly, since the inappropriate use of the Wick
time ordered product is where the "infinities" actually come from).
There's no treatment of distributions or distribution theory in the
book. That's like doing Newtonian Physics without calculus! A
pretty funny situation for a book with "for mathematicians" in the title.
George Jones
As I understand things, the the Langrangian for the Standard Model has
separate global U(1) symmtries that correspond to baryon number, and
to number conservation for each generation of leptons, i.e., a global
U(1)^4 symmetry. This means that these numbers are conserved to any
order in perturbation theory.
However, this U(1)^4 is reduced to U(1) symmetry for B - L by certain
topological (instanton) configuration configurations of the SU(2) field.
Because SU(2) is a spontaneously broken symmetry, baryon number
nonconservation is highly suppressed. At the high energies after the
big bang, SU(2) is a good symmetry, and baryon number nonconservation
is possible within the standard model. See page 475 of Ticciati, page
454 of Weinberg vol. II, or page 434 of the first edition of Ryder.
In some GUTs, the Lagrangian only has a global U(1) symmetry for B - L,
so, even at this level, there is baryon nonconservation.
Regards,
George
George Jones
> In article <3B3C72A2...@yahoo.com> George Jones <george_l...@yahoo.com> writes:
> >Jim Heckman wrote:
> >
> >> Is there a good book that talks about this kind of stuff?
> >
> >The more I look at it, the more I like the book "Quantum Field Theory
> >for Mathematicians" by Robin Ticciati, though at $110, it isn't cheap.
>
> But its whole take on the so-called infinities and divergences is totally
> misleading.
>
> You can do perturbation theory, without divergences of any kind, and
> without the need for renormalization by simply handling the mathematics
> of distributions in the correct fashion (particularly, by defining the
> time ordered product correctly, since the inappropriate use of the Wick
> time ordered product is where the "infinities" actually come from).
As I said, I'm just learniing this stuff, but it appears to me that
Ticciati's presentation is fairly standard. Your beef is not just
with Ticciati, but with much of the physics community. I do not have
the depth of understanding of QFT necessary for comment much beyond this.
I will say that I don't like the divergences are handled, and that my
hopes are equally divided between:
1) QFT will eventually be based on sounder mathematics;
2) the divergences indicate that new physics is needed.
I know from your posts on sci.physics.research that that you think my hope
for 1) has already been accomplished.
It's interesting to note that Feynman always considered QFT's mathematical
handling of infinities to be provisional, and even considered delaying
publication of his work until better techniques were found.
> There's no treatment of distributions or distribution theory in the
> book. That's like doing Newtonian Physics without calculus! A
> pretty funny situation for a book with "for mathematicians" in the title.
Well, I said I didn't like title. I do, however, like the book.
He doesn't treat distributions, but does give an interesting and very
brief motivation for the use of rigged Hilbert spaces in quantum theory.
Besides this, his use of distributions is similar to the that of many
other physics QFT references.
It's interesting that Ticciati's equation (1.4.3) for delta functions
is wrong. I don't think the mistake indicates any lack of understanding
on his part; it's just the type of minor mistake that we all make.
Regards,
George
Uncle Al
Right. My point in
http://www.mazepath.com/uncleal/eotvos.htm
(O7 July revised - with 100-year Earth solar orbit gravitational
acceleration data, and Earth surface inertial centripetal
acceleration fit to the satellite-derived geoid)
is that parity\chirality routinely (approaching "always")
violates conservation in weak interactions (as opposed to Weak
interactions). Gravity is expected to unify with the electroweak
force. One is therefore strongly compelled to test the
Equivalence Principle with parity-violating (mirror-image
intensely chiral) test masses rather than with disparate test
mass compositions.
It's a reasonable proposal. If you are rolling stuff down an
inclined plane, which will be more interesting: beryllium vs.
gold spheres, aluminum spheres vs. aluminum cones? Geometry
interacts with geometry.
Go convince Adelberger or Cowsik. It's like selling condoms in a
nunnery. The problem is politics not need.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
David Evens
Hopkins) wrote:
>In article <tjm097j...@news.supernews.com> "Jim Heckman" <NOjhe...@SPAMmy-deja.com> writes:
>>> Baryon number is a consquence of a global U(1). IIRC, it is exactly
>>> conserved in the standard model.
>>
>>Could you say a little bit more about how this global U(1) for baryon
>>number arises from U(1)xSU(2)xSU(3)?
>
>It doesn't, and it can't come from there or any extension of U(2)xSU(3).
>It's a global symmetry and not a local symmetry.
>
>(Footnote: U(1)xSU(2) = U(2)).
>
>Aside from the 4 quantum numbers contained in U(2)xSU(3), the only
>other (generation-independent) quantum number that can arise from a local
>symmetry is the
> Red + Green + Blue - 3*Lepton
>
>number (or, basically: the Baryon - Lepton number).
>
>Baryon number conservation doesn't come from anywhere and is probably
>false since the net baryon number is a gezillion -- probably evenly
>matched by the net lepton number, which raises a strong suspicion that
>something exists which can convert between baryons and anti-leptons;
>and between leptons and anti-baryons. Something which can only occur
>at superhigh temperature can convert between positrons and protons;
>electrons and anti-protons. Hotter even than the inside of a supernova.
All GUT predict that kind of process occuring in the early universe
when temperatures were still high enough. Of course, the actual
conversions are between leptons and antiquarks and altileptons and
quarks, but they do take advantage of the fact that the universe is
asssymetrical accross the matter-antimatter symetry.
Mark William Hopkins
>As I said, I'm just learniing this stuff, but it appears to me that
>Ticciati's presentation is fairly standard. Your beef is not just
>with Ticciati, but with much of the physics community.
They're more like a rather parochial school of thought -- the "Weinberg"
people than a standard. You can tell them apart from a mile off.
There are about 5-10 such groups I've been able to discern, most under the
illusion that they are the 'standard' or 'majority'. It's almost like
these are political affiliations, like "liberal", "libertarian",
"conservative", "socialist", etc.
Anyway... it's not my beef but the beef of a very large segment of the
physics community, including notably Dirac, Feynman (as you noted);
Bogoliubov & Shirkov; Steinmann (who came out with a monograph in
2000 or 2001 featuring his own infinity-free formulation of QED); Epstein
and Glaser, Scharf and the entire community now engaged in the causal
approach which has recently sprung into major significance; as well as
Colombeau and a large segment of the people involved in Distribution
Theory.
>1) QFT will eventually be based on sounder mathematics;
>2) the divergences indicate that new physics is needed.
After (1) was done, issue (2) became purely chimerical. There's
nothing left to explain or account for nor any need for new physics on
that account. The Physics we have now is sufficient.
Mark William Hopkins
>As I understand things, the the Langrangian for the Standard Model has
>separate global U(1) symmtries that correspond to baryon number, and
>to number conservation for each generation of leptons, i.e., a global
>U(1)^4 symmetry. This means that these numbers are conserved to any
>order in perturbation theory.
And it's still true even in the next to minimal Standard Model in
which neutrinos are represented as ordinary massive 4 component
Dirac spinors, like everyone else; only then it's the U(1) x U(1)
of B & L. These are the "accidental symmetries".
>Because SU(2) is a spontaneously broken symmetry, baryon number
>nonconservation is highly suppressed. At the high energies after the
>big bang, SU(2) is a good symmetry, and baryon number nonconservation
>is possible within the standard model. See page 475 of Ticciati, page
>454 of Weinberg vol. II, or page 434 of the first edition of Ryder.
The Standard Model's "19th parameter". Out of all the references I've
reviewed I've only seen this brought up by the authors you mentioned.
This goes strictly outside of perturbation theory (but the problem
is there isn't really any such thing as a non-perturbative Quantum
Field Theory to go outside to and therefore no basis for any
arguments!).
Even the basic argument, or any argument which makes essential use of the
symmetry breaking concept, is suspect because Electroweak Theory itself can
be constructed and derived without ANY symmetry breaking mechanism or mass
generation mechanism of any kind [1,2,3].
How is the argument to be rendered in terms of the other formulations?
The whole idea of "symmetry breaking" need not be anything more than a
purely mathematical artifact with no physical relevance, to begin with;
whose original invocation was based on some rather weak hand-waving analogies
to other physical systems like magnets (i.e., I think they were grasping at
straws when they first came up with the idea).
So the extrapolations to the non-perturbative realm are iffy, at best;
even granting the existence of some sort of non-perturbative QFT.
References:
[1] "Perturbative gauge invariance: the electroweak theory"
Michael Duetsch, Guenter Scharf
hep-th/9612091
[2] "Perturbative gauge invariance: electroweak theory II"
Andreas Aste, Guenter Scharf, Michael Duetsch
hep-th/9702053
The entire Electroweak Lagrangian (including the Higgs couplings
and Higgs potential) are derived from a newly formulated 2nd
quantized version of gauge invariance called "perturbative gauge
invariance".
[3] General massive gauge theory
Guenter Scharf
hep-th/9901140
The uniqueness of the SU(2) x U(1) + Higgs Lagrangian is proven for
a theory with 3 massive + 1 massless gauge boson + 1 physical scalar.