- #1
smallgirl
- 80
- 0
Ok, so I'd like some advice on doing integrals that involve a laplacian and a tensor for example
[tex]=\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})[/tex]
where [tex] F_{\rho\sigma}[/tex] is the tensor written out as [tex]\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho}[/tex]
[tex]=\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})[/tex]
where [tex] F_{\rho\sigma}[/tex] is the tensor written out as [tex]\partial_{\rho}A_{\sigma}-\partial_{\sigma}A_{\rho}[/tex]