Integrals featuring the laplacian and a tensor

  • Thread starter smallgirl
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  • #1
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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]
 

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  • #2
dextercioby
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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

[tex] \frac{\delta F}{\delta A_{\mu}} \Box F [/tex]
 

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