Abstract
We analytically obtain the spectra of the operators fx443-1 and fx443-1, fx443-1 being the operator in the euclidean space-time R 4 of a fermion interacting chirally with a uniform electromagnetic field. We verify that they are insensitive to (a class of) gauge variations. Only one of those spectra, according to the sign of F μν F ̃ μν , possesses the null eigenvalue, whose multiplicity is the index of fx443-1.
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