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radioactive8
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Homework Statement
Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.
Homework 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:
$$\partial_n \partial^n A^m = \frac{1}{c} J^m$$
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 Am and Am. 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.