Maxwell field quantization in the Coulomb Gauge
FrediFizzx
clarification of what the "elementary misunderstandings" might be if
anyone would like to respond.
"Your posting is inappropriate for sci.physics.research since it
contains
elementary misunderstandings concerning the quantization of the
interacting electromagnetic field."
With kindest regards,
Hendrik van Hees.
Co-moderator for sci.physics.research
On Tuesday 06 April 2010 08:34:22 you wrote:
> "Igor Khavkine" <igo...@gmail.com> wrote in message
> news:0b2e1826-8ef0-49bf...@r1g2000yqb.googlegroups.com
> ...
>
> > On Apr 3, 5:07 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> >> Thus spake Igor Khavkine <igor...@gmail.com>
> >>
> >> >On Apr 2, 7:24 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk>
wrote:
> >> >> So, what we should see is that the interaction Hamiltonian
> >> >> couples a
> >> >> charged particle to the Coulomb field through the mechanism or
> >> >> creating
> >> >> or annihilating a photon.
> >> >
> >> >That's the part that is false. No photon creation or annihilation
> >> >operators appear in the last equation of B&D's section 15.2.
> >>
> >> Reason seems to be that Coulomb gauge is not a full quantisation.
> >
> > I'm sorry, but that is patently false. The widespread use of the
> > Coulomb gauge as well as many fully detailed accounts of it stand
> > as a testament to its validity. Now is a good time to concede the
> > point under discussion above, rather than making dramatic
> > unsubstantiated claims about standard QED methods.
>
> ?? Only the transverse components of the field are quantized in the
> Coulomb gauge so how could that statement be false? Yes, there are
> many scenarios that work just fine with that method. But for sure,
> it is not a *complete* story. How can it be with only part of the
> field quantized?
>
> Best,
>
> Fred Diether
I am adding a quote here from Milonni's "The Quantum Vacuum: An
Introduction to Quantum Electrodynamics",
"As discussed in Section 4.4, only the transverse electromagnetic fields
are quantized in the Coulomb gauge; the longitudinal field is a c-number
whose contribution to the Hamiltonian takes the form of instantaneous
Coulomb interactions among charged particles."
So comparing that statement with what I said, where is the "elementary
misunderstanding"? Weinberg in "The Quantum Theory of Fields, Vol I"
basically says the same thing.
Best,
Fred Diether
Oh No
>The following reply was rejected on SPR so I would like to get some
>more clarification of what the "elementary misunderstandings" might be
>if anyone would like to respond.
>
>"Your posting is inappropriate for sci.physics.research since it
>contains
>elementary misunderstandings concerning the quantization of the
>interacting electromagnetic field."
>
elementary misunderstandings are on the part of the moderator.
I have noted too that Igor's debating style includes snipping the part
of a post which refutes his position and responding as though the
refutation was not given.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
FrediFizzx
news:JBLRoQAi...@charlesfrancis.wanadoo.co.uk...
> Thus spake FrediFizzx <fredi...@hotmail.com>
>>The following reply was rejected on SPR so I would like to get some
>>more clarification of what the "elementary misunderstandings" might be
>>if anyone would like to respond.
>>
>>"Your posting is inappropriate for sci.physics.research since it
>>contains
>>elementary misunderstandings concerning the quantization of the
>>interacting electromagnetic field."
>>
> It seems to me patently clear that what you say is correct, and that
> any
> elementary misunderstandings are on the part of the moderator.
>
> I have noted too that Igor's debating style includes snipping the part
> of a post which refutes his position and responding as though the
> refutation was not given.
Others seem to be doing that also which is actually a very common tactic
on UseNet. This whole debate seems to be that we either accept that
virtual particles (photons in this case) really exist or we have to
accept that static electric fields are fundamental with no photons
involved. Sheesh, ever since high school one learns that photons are
the carriers of the electromagnetic force. I would think that includes
the Coulomb force also which is just a special case of the Lorentz force
with v and B set to zero.
However, this is actually very interesting when you get down to the
details. Problem is that the Coulomb field has no time dependence so
can't have your normal creation and annihilation operators that depend
on time to quantize the field directly. But that is assuming that
microscopically the field is still static which it most likely isn't
since we have the Uncertainty Principle to consider. :-) And we also
know that v and B would most likely not be zero microscopically.
Bottom line seems to be that the "virtual particle" dissenters are also
rejecting the Uncertainty Principle.
Best,
Fred Diether
maxwell
> "Oh No" <N...@charlesfrancis.wanadoo.co.uk> wrote in message
>
> news:JBLRoQAi...@charlesfrancis.wanadoo.co.uk...
>
>
>
>
>
> > Thus spake FrediFizzx <fredifi...@hotmail.com>
Coulomb's "law" is an experimental summarization of the interactions
of gazillions of electrons distributed over two macroscopic objects
separated by macroscopic distances with the "force' results inferred
over macroscopic time-scales. Assuming that these macroscopic
averages apply at the level of unit charges (e.g. electrons) is an
unwarranted (but vastly simplifying assumption). It would like trying
to predict the annual incomes of EACH and every (distinct) US citizen
from the GNP. The math of averages is a one-way relationship: details
to averages - not the inverse.
Accordingly, assuming that Coulomb's "law" is even as fundamental as
the rest of Maxwell's (statistical) Equations is just the kind of
error that Maxwell himself made when he incorporated this "law" into
his study of magnetism.
Gentlemen, it is time to start challenging the assumptions!!
Bob_for_short
>
> > I have noted too that Igor's debating style includes snipping the part
> > of a post which refutes his position and responding as though the
> > refutation was not given.
>
I also suffer from his behaviour.
> Problem is that the Coulomb field has no time dependence so
> can't have your normal creation and annihilation operators that depend
> on time to quantize the field directly.
No, the Coulomb potential term 1/|r2(t) - r1(t)| depends on time
throught the time-dependent distance. As soon as it is explicitely
expressed via other dynamic variables, this term is not an
"independent" degree of freedom, unlike the transversal part of EMF.
>
> Bottom line seems to be that the "virtual particle" dissenters are also
> rejecting the Uncertainty Principle.
>
Not at all. QM automatically takes into account the wave features
including HUP. On the contrary, it is quite wrong to think in terms of
localized and separated "particles" instead of spread and overlapping
waves in analysis of interactions.
FrediFizzx
news:ac11193e-ead7-48ab...@w17g2000yqj.googlegroups.com...
> On 8 avr, 04:07, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> Problem is that the Coulomb field has no time dependence so
>> can't have your normal creation and annihilation operators that
>> depend
>> on time to quantize the field directly.
>
> No, the Coulomb potential term 1/|r2(t) - r1(t)| depends on time
> throught the time-dependent distance. As soon as it is explicitely
> expressed via other dynamic variables, this term is not an
> "independent" degree of freedom, unlike the transversal part of EMF.
OK, how do you quantize that? :-) You can model as virtual particles if
you go the other way around.
>> Bottom line seems to be that the "virtual particle" dissenters are
>> also
>> rejecting the Uncertainty Principle.
>>
> Not at all. QM automatically takes into account the wave features
> including HUP. On the contrary, it is quite wrong to think in terms of
> localized and separated "particles" instead of spread and overlapping
> waves in analysis of interactions.
Not really what I mean. Of course any "wave features" have uncertainty
automatically. What I mean is that the HUP allows the Einstein relation
to be violated.
Best,
Fred Diether
Bob_for_short
> "Bob_for_short" <vladimir.kalitvian...@wanadoo.fr> wrote in message
>
> news:ac11193e-ead7-48ab...@w17g2000yqj.googlegroups.com...
>
> > On 8 avr, 04:07, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> >> Problem is that the Coulomb field has no time dependence so
> >> can't have your normal creation and annihilation operators that
> >> depend
> >> on time to quantize the field directly.
>
> > No, the Coulomb potential term 1/|r2(t) - r1(t)| depends on time
> > expressed via other dynamic variables, this term is not an
> > "independent" degree of freedom, unlike the transversal part of EMF.
>
> OK, how do you quantize that? :-) You can model as virtual particles if
> you go the other way around.
In Heisenberg representation r2(t) and r1(t) are operators with their
quantum dynamics. The Coulomb potential term 1/|r2(t) - r1(t)| is a
"function" of these operators. No separate quantization is necessary
for such an explicit function.
In Schroedinger representation, say in Hydrogen, the average (mean)
value of 1/r is "quantized" together with the total energy
quantization.
Another thing is that in the Lorentz gauge with formally four degrees
of freedom one may think of "exchange" with virtual photons but this
temptation appears only in the perturbative treatment of scattering.
It is not clear at all what the _exact_ equations say in this gauge
(too complicated set of coupled equations).