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Varying the action with respect to A_\mu

  1. Nov 30, 2014 #1
    Was reading a paper and trying to work out the author's calculations: I am trying to vary the action,
    $$S_A= \int d^3x \left[ \, -\frac{1}{4}F_{\mu\nu}(A)F^{\mu\nu}(A) +\frac{1}{2}m\, \epsilon^{\mu\nu\rho}A_\mu F_{\nu\rho}(A) \right] $$

    with respect to $$A_\mu$$. I am finding difficulty deriving this because $$A_\mu$$ is embedded in $$F_{\mu \nu}$$. So my attempt was writing this all in terms of $$A_\mu$$:

    $$S_A= \int d^3x \, \left[ -\frac{1}{4}(\partial_\mu A_\nu - \partial_\nu A_\mu) (\partial^\mu A^\nu - \partial^\nu A^\mu) +\frac{1}{2}m\, \epsilon^{\mu\nu\rho}A_\mu (\partial_\nu A_\rho - \partial_\rho A_\nu) \right] $$ and then I got stuck. If you could please lead me from here.

    Reference, section 2: http://arxiv.org/pdf/hep-th/9705122.pdf
  2. jcsd
  3. Dec 5, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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