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Electromagnetic field equations of motion

  1. Oct 6, 2013 #1
    1. I'm not quite sure how the laplacian acts on this integral



    2. [tex]\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})[/tex]



    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 [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})+\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})[/tex]
     
    Last edited: Oct 6, 2013
  2. jcsd
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