# Gauge choice for a magnetic vector potential

Lodeg
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?

Lodeg
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?

Gold Member
2022 Award
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
$$\frac{1}{c} \partial_t \Phi + \vec{\nabla} \cdot \vec{A}=0 \qquad \text{(Lorenz gauge)},$$
$$\vec{\nabla} \cdot \vec{A}=0 \qquad \text{(Coulomb gauge)}.$$

Lodeg
In that case, would a condition like ∫∫ A x F(r,t) dS = 0 , be acceptable as a guage?

Lodeg
More generally, could a condition like ∫∫ L(A) x F(r,t) dS = 0 be a gauge, where L is a linear operator?

Gold Member
2022 Award
I've never seen gauge-constraints involving integrals. This looks very complicated. What do you think it may be good for?

Lodeg
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?