The discussion centers on the application of the Euler-Lagrange equations to derive the equations of motion (EoM) for electromagnetic fields, specifically focusing on the properties of the antisymmetric tensor \( F_{\mu \nu} \). Participants clarify that for an antisymmetric tensor, all diagonal entries, including \( F_{00} \) and \( F_{ii} \), must equal zero. This conclusion is supported by equation (9) in the attached solution, which explicitly demonstrates the antisymmetry of \( F_{\mu \nu} \).
PREREQUISITESStudents of physics, particularly those studying electromagnetism, theoretical physicists, and anyone interested in the mathematical foundations of field theory.
TSny said:
Yes. The expression for ##F_{\mu \nu}## in (9) shows that ##F## is antisymmetric. In particular, if you let ##\mu = 0## and ##\nu = 0## in the expression for ##F_{\mu \nu}## in (9) then you see that ##F_{00} = 0##.binbagsss said:
