Gauge Freedom of Magnetic Potential in Electrodynamics

[touqra]

Hi,

In Electrodynamics, one often state about the gauge freedom of the magnetic potential. And so, we may choose to impose for example the Coulomb gauge, where the divergence of the potential is zero. But, isn't this only true if there exist no changing electrical field,
\frac{\partial E}{\partial t} = 0 as in the magnetostatics case ? Why would it be called a freedom then, if this is situation dependent ?

Thanks.

 

[Simon Bridge]

http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.

 

[touqra]

http://en.wikipedia.org/wiki/Gauge_fixing
Your choice of gauge it is best to fix is restricted by the physics - yep.
However, the physics described in the coulomb gauge may also be described in the lorentz gauge, or some other, so you are free to choose. Best practice is to choose the gauge that makes the math easier.

Hence, I pointed out there exist no changing electric field or potential. If this is the case, the Lorentz gauge would reduced to the Coulomb gauge. So, essentially, there is only one gauge, i.e. the Lorentz gauge. And this will get reduced to "any" gauge according to the situation. I still don't see why the list of gauges and freedoms to choose from.

 

[almarto]

The Coulomb gauge is the more useful for the non-covariant theory, having particular advantages for slow-moving particles. Another choice, the Lorentz gauge, is for the covariant theory. The fields, and Maxwell's equations, are unaffected by gauge. This is the main difference.

 

[Simon Bridge]

iirc: there are an arbitrary number of gauges - see the link: it includes a description of what is meant by "gauge freedom".