What is 4-Vector Potential Transformation under Gauge Fixing?

[Kulkarni Sourabh]

Homework Statement

4- vector potential transformation under Gauge fixing.

Relevant Equations

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What is 4- vector potential transformation under Gauge fixing ?

 

[Grelbr42]

A gauge transform is a change in the 4-vector potential that leaves the $E$ and $B$ fields unchanged. So, for example, consider the 3-vector part of $A$. Since the $B$ field is the curl of the 3-vector part of $A$, then changing $A$ by adding a 3-vector with zero curl does not change $B$.

Gauge fixing means to select particular conditions on $A$ to simplify the calculations you are currently doing. You do this by adding the corresponding things to $A$ such that the required condition is true. There are a number of commonly used gauge fixing conditions.

They are useful because we usually express the original version of the equations in a gauge-invariant (or covariant) form. That means we write all the equations in such a way that they are still true regardless of the gauge conditions we apply. That means if we were to do the calculation in another gauge we would necessarily get the same answer. Assuming, of course, we didn't make a mistake.