# Maxwell Lagrangian at weak fields

1. Dec 6, 2014

### PhyAmateur

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".

2. Dec 6, 2014

### Staff: Mentor

Imagine the case of no field at all. Everything apart from the constant is zero, so the constant has to be zero as well.