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Integrals featuring the laplacian and a tensor

  1. Oct 6, 2013 #1
    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]
  2. jcsd
  3. Oct 7, 2013 #2


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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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