# Integrals featuring the laplacian and a tensor

1. Oct 6, 2013

### smallgirl

Ok, so I'd like some advice on doing integrals that involve a laplacian and a tensor for example

$$=\int\frac{\delta}{\delta A_{\mu}}\frac{1}{4M^{2}}(\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho})\frac{\partial^{2}}{\partial x^{2}}(\partial^{\rho}A^{\sigma}-\partial^{\sigma}A^{\rho})$$

where $$F_{\rho\sigma}$$ is the tensor written out as $$\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho}$$

2. Oct 7, 2013

### dextercioby

The integration is not an issue. Actually you left out the integrating element. You must be having a functional differentiation of a 4-order derivative term shorthandedly written F box F. Since box F has triple space-time derivatives, it would yield completely 0 under functional differentiation. So you only have

$$\frac{\delta F}{\delta A_{\mu}} \Box F$$