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There's been quite a while since reading some serious physics, so i forgot some key points. The question I'm about to ask may seem trivial for a knowledgeable person, but I can't find the answer and I thought it is easier to get a right answer here, than wondering through a dozen of QFT books.
So here goes:
Why does the term
[tex] \frac{e}{2} \bar{\Psi} (x) \Sigma^{\mu\nu} F_{\mu\nu}(x) \Psi (x)[/tex]
NOT appear in the classical lagrangian for the spin 1/2 parity invariant electrodynamics ?
p.s. I hope the notation is obvous, Sigma is the spin matrix = <i/2> times the commutator of the gamma matrices, the F is the e-m field tensor and the big Psi-s are the Dirac spinors.
So here goes:
Why does the term
[tex] \frac{e}{2} \bar{\Psi} (x) \Sigma^{\mu\nu} F_{\mu\nu}(x) \Psi (x)[/tex]
NOT appear in the classical lagrangian for the spin 1/2 parity invariant electrodynamics ?
p.s. I hope the notation is obvous, Sigma is the spin matrix = <i/2> times the commutator of the gamma matrices, the F is the e-m field tensor and the big Psi-s are the Dirac spinors.