(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.

2. Relevant equations

The form of the L. density is:

$$L=-\frac{1}{2} (\partial_n A_m)(\partial^n A^m) - \frac{1}{c} J_m A^m$$

where J is the electric current.

The result has to be:

$$\partial_n \partial^n A^m = \frac{1}{c} J^m$$

3. The attempt at a solution

Using the Euler- Lagrange equations that derive the eq. of motion I do not understant if I have to treat the fields A^{m}and A_{m}. In addition, the Euler Lagrange equations from a L.density of the form:

$$L=-\frac{1}{2} (\partial_n A_m)(\partial_n A_m) - \frac{1}{c} J_m A^m$$

giveaway the wanted result. But I could not relate the two L.densities.

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# Homework Help: Derivation of the Eqation of Motion from Fermi Lagrangian density

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