4- vector potential transformation

In summary, a gauge transform involves changing the 4-vector potential while keeping the electric and magnetic fields unchanged. Gauge fixing is the process of selecting conditions on the 4-vector potential to simplify calculations. This is done by adding corresponding terms to the 4-vector potential to make the required condition true. Gauge fixing is useful because the original equations are usually expressed in a gauge-invariant form, meaning they will still hold true regardless of the gauge conditions applied.
  • #1
Kulkarni Sourabh
2
1
Homework Statement
4- vector potential transformation under Gauge fixing.
Relevant Equations
.
What is 4- vector potential transformation under Gauge fixing ?
Screenshot_2023_0220_150437.png
Screenshot_2023_0220_150520.png
 
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  • #2
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.
 
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