# Electromagnetic field equations of motion

1. Oct 6, 2013

### smallgirl

1. I'm not quite sure how the laplacian acts on this integral

2. $$\frac{\delta S}{\delta A_{\mu}}=\int\frac{\delta}{\delta A_{\mu}}(\frac{1}{4}F_{\rho\sigma}\frac{\triangle}{M^{2}}F^{\rho\sigma})$$

3. I know I have to split the integral into three integrals for x y and z, but I'm not sure if
a) I should write out F in full,
b) If the laplacian only acts on the second F or both, and if so how for each instance

I have got this anyways $$=\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial x^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})+\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial y^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})+\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial z^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})$$

Last edited: Oct 6, 2013