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Mark99

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- TL;DR Summary
- Dual field strength tensor and EOM

Hello everybody! I know in classical field theory adding in the Lagrangian density a term of the form F

In particular I get ∂(F

Thank you in advance.

_{αβ}(*F)^{αβ}(where by * we denote the dual of the field strength tensor) does not change the EOM, since this corresponds to adding a total derivative term to the action. However when computing the EOMs explicitly through ∂_{μ}(∂L/∂∂_{μ}A_{υ})-∂L/∂A_{υ}=0, I do not find this to be true.In particular I get ∂(F

_{αβ}(*F)^{αβ})/∂∂_{μ}A_{ν}=4(*F^{μν}), when the result should be zero. I suppose I am not managing the Levi Civita tensor properly, but I do not understand my mistake. Is there someone who can do this derivation explicitly and show it is zero?Thank you in advance.