PhyAmateur
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In http://arxiv.org/abs/hep-th/9506035 the author said after writing this equation:
$$\frac{1}{4}\eta^{\mu\nu\lambda\rho} F_{\mu\nu}F_{\lambda\rho} = \eta_{\sigma\tau\alpha\beta}\frac{\partial L}{\partial F_{\sigma\tau}} \frac{\partial L}{\partial F_{\alpha\beta} } + 2C$$
where C was arbitrary constant of integration." In fact, if L is to agree with the usual Maxwell Lagrangian at weak fields the constant must vanish". Why? I mean why should the constant vanish. It seems that I don't understand what he meant by Maxwell Lagrangian at "weak fields".
$$\frac{1}{4}\eta^{\mu\nu\lambda\rho} F_{\mu\nu}F_{\lambda\rho} = \eta_{\sigma\tau\alpha\beta}\frac{\partial L}{\partial F_{\sigma\tau}} \frac{\partial L}{\partial F_{\alpha\beta} } + 2C$$
where C was arbitrary constant of integration." In fact, if L is to agree with the usual Maxwell Lagrangian at weak fields the constant must vanish". Why? I mean why should the constant vanish. It seems that I don't understand what he meant by Maxwell Lagrangian at "weak fields".