QED with vector and axial vector types of interaction and dynamical generation of particle masses

Abstract

We consider a model of electrodynamics with two types of interaction, the vector $(e\bar \psi (\gamma ^\mu A_\mu )\psi )$ and axial vector $(e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )$ interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ⊗ U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B _μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B _μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B _μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B _03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.