- #1

jacobrhcp

- 169

- 0

**[SOLVED] invariance of maxwell's equations under Gauge transformation**

## Homework Statement

Show that the source-free Maxwell equations [tex]\partial_{\mu} F^{\mu\nu}=0[/tex] are left invariant under the local gauge transformation

[tex] A_{\mu}(x^{\nu})\rightarrow A'_{\mu}(x^{\nu})=A_{\mu}(x^{\nu})+\frac{\partial}{\partial x^{\mu}}\varphi(x^{\nu}) [/tex]

for an arbitrary scalar function [tex]\varphi(x^{\nu})[/tex]

## Homework Equations

The definition of the field strength tensor: [tex]F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}[/tex]

## The Attempt at a Solution

This is a course I don't quite have the foreknowledge of. There is no book, so some things I can't quite figure out. The teacher gave the solution on the blackboard already, so that's not the real problem. I wrote it down real good and neat, but I don't get it at all.

I just don't know what a Gauge transformation is, or what the definition of maxwell's equation in that tensor is, I've only seen it as four equations just yet (both integral and differential form). If someone could just help me understand the problem, or give me some useful links to understand it, I'd appreciate it a lot... or mainly what the bigger part of those symbols mean.

Last edited: