Induced B wedge F term and photon mass generation in (3+1) dimensions

Analyzing a (3+1)-dimensional model with four-fermi interactions, we show that topological B∧F terms (both Abelian and non-Abelian) can be induced radiatively by massive fermions at the one-loop level. It is further pointed out that a mechanism of photon (or non-Abelian gauge field) mass generation distinct from the usual Higgs mechanism, through the B∧F term, is also implemented in the long distance effective action of this model, provided a gap equation is satisfied.