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