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Would not a more accurate nomenclature be (divA = 0) for the Coulomb gauge and (divA = 0 together with scalar potential = 0) for the radiation gauge? The radiation gauge, which is used in perturbative calculations, is just the Coulomb gauge in the absence of charge and describes the free electromagnetic field. The Coulomb gauge, in the presence of charge and accordingly with non-zero scalar potential, is used in quantum chemistry. Xxanthippe 09:28, 19 June 2006 (UTC)
Hi, I think this reference does a good job in explaining the concepts, at least for maxwell's equations. http://www.mathematik.tu-darmstadt.de/~bruhn/Maxwell-Theory.html
What is meant by "redundant degree of freedom"
What is an "equivalence class"
What is "configuration space"
What calculations do gauge fixing simplify? What calculations don't gauge fixing simplify?
And if you could settle an argument for me, is gauge fixing compatible with the Lorentz Transformations?
Also, what is "manifest" Lorentz Invariance, and how does that compare to regular Lorentz Invariance?
"This was not well understood at first even by active researchers in the field[1] and remains inconspicuous in most textbook treatments, partly because a rigorous derivation of the photon propagator requires deeper mathematical tools than one needs for the rest of QED." This is cryptic, even POVish. The note leads nowhere. Clarification please! Xxanthippe 23:54, 5 January 2007 (UTC)
The Lorenz Gauge has its own article which repeats most of the material here. It might make sense to either use one big article with all the gauges or give other gauges their own articles. Also, mixing four dimensional formulations with three dimensional formulations is confusing because almost-similar notation actally means different things. It would be much nicer to see all the three dimensional formulations in one article and then the four dimensional formulations together in a separate article so the reader always sees one "world view" at a time.
Have to be more careful with wording here- we do not completely pull the ward identity out of our ass and 'enforce' it as the article implies- to my knowledge we can either have the current or axial current conserved and we choose the current, by our renormalization prescription, to be conserved which leads to the ward identity. —Preceding unsigned comment added by 128.230.52.201 ( talk) 00:03, 10 February 2009 (UTC)
The Intro and section on Gauge Freedom with the illustrative diagram provides exactly the kind of gentle introduction that I was seeking. Thanks! But something puzzles me. Why is is the term "gauge" used? The term gauge implies that something is being measured carefully or that a scale is being assigned to something needing to be quantified, but it seems that this process has no effect on the physical quantities described by the field theory. Simple is better ( talk) 18:54, 15 August 2009 (UTC)
Thank you for your help! Simple is better ( talk) 19:07, 16 August 2009 (UTC)
Because the Coulomb gauge is used almost universally in quantum chemistry and condensed matter physics I have rewritten this section to extend it and include recent material. Xxanthippe ( talk) 09:27, 10 March 2010 (UTC).
The existence of arbitrary numbers of gauge functions \psi(\mathbf{x},t), corresponds to the U(1) gauge freedom of this theory.
Could it be made clearer why it is a U(1) freedom in particular? 151.200.120.52 ( talk) 02:18, 20 May 2010 (UTC)
>To suppress the "unphysical" longitudinal and time-like polarization states, which are not observed in experiments at classical distance scales,
Has anybody tried to determine what these longitudinal and time-like waves would look like, or done any experiments investigating their existence?
98.154.22.134 ( talk) 10:18, 21 March 2013 (UTC)
I noticed a little ambiguity in defining the Coulomb gauge.
My guess is that the real definition is the first, incomplete definition, since it is universal and gets us the properties we want. The integral definition is nice but it is more strict and does not necessarily equal all electromagnetic potentials that can we call "Coulomb gauge". Am I right in this thinking? It is after all what we present on Mathematical_descriptions_of_the_electromagnetic_field#Coulomb_gauge. If so I'd like to bring over some of the more general equations from that article in order to bring this section into analogous parity with Lorentz gauge, and separate the special Coulomb-integral gauge into a subsection.
Likewise a small discussion of what are the remaining freedoms in the Coulomb gauge, is worth including. If I got it right, this freedom is that any gauge transformation satisfying is valid. (Which is a bit weird, since there is no restriction in the time-dependence!) -- Nanite ( talk) 18:48, 7 December 2016 (UTC)
@ Xxanthippe: I had completely forgotten about our discussion above, until just this moment. :D Sorry if I seem to be blundering in again! What do you think about moving the Coulomb gauge stuff into its own article, to put it on a level footing with the Lorenz gauge? It seems there is more to say on the topic, for example the explanation (e.g. in Jackson's Electrodynamics) for why it is called 'transverse gauge', 'radiation gauge', etc. And, we can leave a summary here as a residue. I am inclined to do this but I'm curious your opinion. -- Nanite ( talk) 00:02, 6 January 2021 (UTC)
I'm not sure about the "incompleteness" attribute stated on the temporal/Hamiltonian/Weyl gauge. Given that one can always perform a gauge transformation that takes where is the gauge transformation function, one can always find a to ensure that by solving the differential equation, , as long as is continuous in time (as it is). Therefore, it is complete. If there is a formal reason for it being incomplete, a citation would be useful, because it is not obvious. — Preceding unsigned comment added by Pflammer ( talk • contribs) 15:55, 7 December 2018 (UTC)
I think the article should make the difference between Landau gauge for low energy calculations like in the Landau levels, and the Landau gauge presented here. But I do not know if they are related somehow.-- ReyHahn ( talk) 12:06, 10 September 2020 (UTC)
Point 5 in the Coulomb Gauge paragraph is a great result: "The Coulomb gauge admits a natural Hamiltonian formulation of the evolution equations of the electromagnetic field interacting with a conserved current". I think this is very little known, even in the specialist community. I could find no reference on this point, although I arrived at the same conclusion in a particular case ( https://doi.org/10.1209/0295-5075/103/28004). A reference in the present wikipedia article is definitely needed. 192.54.145.139 ( talk) 09:13, 10 June 2023 (UTC)
In the text one can read « Not until the advent of quantum field theory could it be said that the potentials themselves are part of the physical configuration of a system. » I argue that this is false. Just after this the Aharonov-Bohm effect is mentioned, which can be described by a nonrelativistic Schrödinger equation (where the hamiltonian is the quantum Lorentz force hamiltonian) for a particle coupled with classical electromagnetic scalar and vector potentials. Historically it is true that this was discovered after the advent of quantum field theory (and quantum electrodynamics) but we cannot affirm that it could not have been said before that advent that the potentials are physical (in the sense used here of "measurable"). It is conceivable that the Schrödinger equation for the Lorentz force would have been studied and that physicists would have found the Aharonov-Bohm effect before QED and QFT. Of course there is only one reality, one history, so if when we say "could be" we mean "was", then the text is right, but this is not what is usually implied by the formulation used in the text: usually when we hypothesize what could have been, we have some simple model of the world where we imaginarily tweak parameters (events) and imagine the consequences; and i think that imagining possible alternative histories of the discovery of the physicality of electromagnetic potentials we can reasonably argue that it could have been said that they are physical before QFT. Thus i suggest changing this sentence to, for instance, « It was only after the advent of quantum field theory that physicists discovered that the potentials themselves are part of the physical configuration of a system. » We can date the concept of QFT and QED to 1927 by Dirac, or perhaps to Born-Heisenberg-Jordan in 1926 for free QFT, so that would have left very little time, in 1925 and 1926, to write the Lorentz-force Schrödinger equation and derive a physical effect of the potentials before the advent of QFT, but still i think my point is valid. Plm203 ( talk) 22:53, 14 August 2023 (UTC)
yes it is interesting that the two gauges might be identical in special cases, but does that observation really belong in a section devoted to essential properties of Coulomb gauge? I apologize for provocative title, but I can see where a beginning student could get that misconception from a casual reading of item four of Coulomb gauge section. I suggest that it be carefully reworded to make the invention more clear. EternalStudent2000 ( talk) 15:18, 21 November 2023 (UTC)
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Would not a more accurate nomenclature be (divA = 0) for the Coulomb gauge and (divA = 0 together with scalar potential = 0) for the radiation gauge? The radiation gauge, which is used in perturbative calculations, is just the Coulomb gauge in the absence of charge and describes the free electromagnetic field. The Coulomb gauge, in the presence of charge and accordingly with non-zero scalar potential, is used in quantum chemistry. Xxanthippe 09:28, 19 June 2006 (UTC)
Hi, I think this reference does a good job in explaining the concepts, at least for maxwell's equations. http://www.mathematik.tu-darmstadt.de/~bruhn/Maxwell-Theory.html
What is meant by "redundant degree of freedom"
What is an "equivalence class"
What is "configuration space"
What calculations do gauge fixing simplify? What calculations don't gauge fixing simplify?
And if you could settle an argument for me, is gauge fixing compatible with the Lorentz Transformations?
Also, what is "manifest" Lorentz Invariance, and how does that compare to regular Lorentz Invariance?
"This was not well understood at first even by active researchers in the field[1] and remains inconspicuous in most textbook treatments, partly because a rigorous derivation of the photon propagator requires deeper mathematical tools than one needs for the rest of QED." This is cryptic, even POVish. The note leads nowhere. Clarification please! Xxanthippe 23:54, 5 January 2007 (UTC)
The Lorenz Gauge has its own article which repeats most of the material here. It might make sense to either use one big article with all the gauges or give other gauges their own articles. Also, mixing four dimensional formulations with three dimensional formulations is confusing because almost-similar notation actally means different things. It would be much nicer to see all the three dimensional formulations in one article and then the four dimensional formulations together in a separate article so the reader always sees one "world view" at a time.
Have to be more careful with wording here- we do not completely pull the ward identity out of our ass and 'enforce' it as the article implies- to my knowledge we can either have the current or axial current conserved and we choose the current, by our renormalization prescription, to be conserved which leads to the ward identity. —Preceding unsigned comment added by 128.230.52.201 ( talk) 00:03, 10 February 2009 (UTC)
The Intro and section on Gauge Freedom with the illustrative diagram provides exactly the kind of gentle introduction that I was seeking. Thanks! But something puzzles me. Why is is the term "gauge" used? The term gauge implies that something is being measured carefully or that a scale is being assigned to something needing to be quantified, but it seems that this process has no effect on the physical quantities described by the field theory. Simple is better ( talk) 18:54, 15 August 2009 (UTC)
Thank you for your help! Simple is better ( talk) 19:07, 16 August 2009 (UTC)
Because the Coulomb gauge is used almost universally in quantum chemistry and condensed matter physics I have rewritten this section to extend it and include recent material. Xxanthippe ( talk) 09:27, 10 March 2010 (UTC).
The existence of arbitrary numbers of gauge functions \psi(\mathbf{x},t), corresponds to the U(1) gauge freedom of this theory.
Could it be made clearer why it is a U(1) freedom in particular? 151.200.120.52 ( talk) 02:18, 20 May 2010 (UTC)
>To suppress the "unphysical" longitudinal and time-like polarization states, which are not observed in experiments at classical distance scales,
Has anybody tried to determine what these longitudinal and time-like waves would look like, or done any experiments investigating their existence?
98.154.22.134 ( talk) 10:18, 21 March 2013 (UTC)
I noticed a little ambiguity in defining the Coulomb gauge.
My guess is that the real definition is the first, incomplete definition, since it is universal and gets us the properties we want. The integral definition is nice but it is more strict and does not necessarily equal all electromagnetic potentials that can we call "Coulomb gauge". Am I right in this thinking? It is after all what we present on Mathematical_descriptions_of_the_electromagnetic_field#Coulomb_gauge. If so I'd like to bring over some of the more general equations from that article in order to bring this section into analogous parity with Lorentz gauge, and separate the special Coulomb-integral gauge into a subsection.
Likewise a small discussion of what are the remaining freedoms in the Coulomb gauge, is worth including. If I got it right, this freedom is that any gauge transformation satisfying is valid. (Which is a bit weird, since there is no restriction in the time-dependence!) -- Nanite ( talk) 18:48, 7 December 2016 (UTC)
@ Xxanthippe: I had completely forgotten about our discussion above, until just this moment. :D Sorry if I seem to be blundering in again! What do you think about moving the Coulomb gauge stuff into its own article, to put it on a level footing with the Lorenz gauge? It seems there is more to say on the topic, for example the explanation (e.g. in Jackson's Electrodynamics) for why it is called 'transverse gauge', 'radiation gauge', etc. And, we can leave a summary here as a residue. I am inclined to do this but I'm curious your opinion. -- Nanite ( talk) 00:02, 6 January 2021 (UTC)
I'm not sure about the "incompleteness" attribute stated on the temporal/Hamiltonian/Weyl gauge. Given that one can always perform a gauge transformation that takes where is the gauge transformation function, one can always find a to ensure that by solving the differential equation, , as long as is continuous in time (as it is). Therefore, it is complete. If there is a formal reason for it being incomplete, a citation would be useful, because it is not obvious. — Preceding unsigned comment added by Pflammer ( talk • contribs) 15:55, 7 December 2018 (UTC)
I think the article should make the difference between Landau gauge for low energy calculations like in the Landau levels, and the Landau gauge presented here. But I do not know if they are related somehow.-- ReyHahn ( talk) 12:06, 10 September 2020 (UTC)
Point 5 in the Coulomb Gauge paragraph is a great result: "The Coulomb gauge admits a natural Hamiltonian formulation of the evolution equations of the electromagnetic field interacting with a conserved current". I think this is very little known, even in the specialist community. I could find no reference on this point, although I arrived at the same conclusion in a particular case ( https://doi.org/10.1209/0295-5075/103/28004). A reference in the present wikipedia article is definitely needed. 192.54.145.139 ( talk) 09:13, 10 June 2023 (UTC)
In the text one can read « Not until the advent of quantum field theory could it be said that the potentials themselves are part of the physical configuration of a system. » I argue that this is false. Just after this the Aharonov-Bohm effect is mentioned, which can be described by a nonrelativistic Schrödinger equation (where the hamiltonian is the quantum Lorentz force hamiltonian) for a particle coupled with classical electromagnetic scalar and vector potentials. Historically it is true that this was discovered after the advent of quantum field theory (and quantum electrodynamics) but we cannot affirm that it could not have been said before that advent that the potentials are physical (in the sense used here of "measurable"). It is conceivable that the Schrödinger equation for the Lorentz force would have been studied and that physicists would have found the Aharonov-Bohm effect before QED and QFT. Of course there is only one reality, one history, so if when we say "could be" we mean "was", then the text is right, but this is not what is usually implied by the formulation used in the text: usually when we hypothesize what could have been, we have some simple model of the world where we imaginarily tweak parameters (events) and imagine the consequences; and i think that imagining possible alternative histories of the discovery of the physicality of electromagnetic potentials we can reasonably argue that it could have been said that they are physical before QFT. Thus i suggest changing this sentence to, for instance, « It was only after the advent of quantum field theory that physicists discovered that the potentials themselves are part of the physical configuration of a system. » We can date the concept of QFT and QED to 1927 by Dirac, or perhaps to Born-Heisenberg-Jordan in 1926 for free QFT, so that would have left very little time, in 1925 and 1926, to write the Lorentz-force Schrödinger equation and derive a physical effect of the potentials before the advent of QFT, but still i think my point is valid. Plm203 ( talk) 22:53, 14 August 2023 (UTC)
yes it is interesting that the two gauges might be identical in special cases, but does that observation really belong in a section devoted to essential properties of Coulomb gauge? I apologize for provocative title, but I can see where a beginning student could get that misconception from a casual reading of item four of Coulomb gauge section. I suggest that it be carefully reworded to make the invention more clear. EternalStudent2000 ( talk) 15:18, 21 November 2023 (UTC)