# Lorentz condition

1. Oct 4, 2009

### nicksauce

1. The problem statement, all variables and given/known data
Given the Lagrangian
$$L = -\frac{1}{2}\partial_{\alpha}A_{\beta}\partial^{\alpha}A^{\beta} + \frac{1}{2}\partial_{\alpha}A^{\alpha}\partial_{\beta}A^{\beta} + \frac{\mu^2}{2}A_{\beta}A^{\beta}$$

show that A satisfies the Lorentz condition $\partial_{\alpha}A^{\alpha} = 0$.

2. Relevant equations

3. The attempt at a solution
I want to say we can treat $\partial_{\alpha}A^{\alpha}$ as an independent field, and find the appropriate field equations for it, but I'm not sure if that makes sense. Any thoughts?

2. Oct 4, 2009

### nicksauce

Upon further thought, this seems like a good time to use Noether's theorem...

3. Nov 11, 2010

### orentago

Last edited by a moderator: Apr 25, 2017