Gauge choice for a magnetic vector potential

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How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ?
Specifically, could a relation in the form A x F(r,t) be a gauge , where F is an arbitrary vector field?
 

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  • #2
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How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ?
Specifically, could a relation in the form: A x F(r,t) = 0, be a gauge , where F is an arbitrary vector field?
 
  • #3
vanhees71
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This looks a bit too much constrained, because it practically says that ##\vec{A}=\lambda \vec{F}##, but you can impose only one "scalar" condition like
$$\frac{1}{c} \partial_t \Phi + \vec{\nabla} \cdot \vec{A}=0 \qquad \text{(Lorenz gauge)},$$
$$\vec{\nabla} \cdot \vec{A}=0 \qquad \text{(Coulomb gauge)}.$$
 
  • #4
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In that case, would a condition like ∫∫ A x F(r,t) dS = 0 , be acceptable as a guage?
 
  • #5
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More generally, could a condition like ∫∫ L(A) x F(r,t) dS = 0 be a gauge, where L is a linear operator?
 
  • #6
vanhees71
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I've never seen gauge-constraints involving integrals. This looks very complicated. What do you think it may be good for?
 
  • #7
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This allows simplifying some expressions.

Are there any criteria to judge the validity of such a condition?

Are there any reference that mention different gauge conditions other than Coulomb and Lorenz conditions?
 
  • #8
vanhees71
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Well, if it helps you with a concrete example, the only validation is to check that the final solutions for the physical fields, ##\vec{E}## and ##\vec{B}##, really solve the problem. In the literature there are also more gauge fixing conditions, particularly in QFT. Some simple ones are temporal gauge, ##A^0=0##, or axial gauge ##A^3=0##, and also the ##R_{\xi}## gauges, based on the action principle rather than a specific constraint for the gauge fields. There are also some more less common ones. See

https://en.wikipedia.org/wiki/Gauge_fixing
 
  • #9
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Thank you very much
 

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