Induced Chern-Simons-like action in Lorentz-violating massless QED

Abstract

In the present work, we study different aspects of Lorentz and CPT symmetry violation in extended massless QED. By following the observation that the $2+1$-dimensional Maxwell-Chern-Simons theory can be originated from the $3+1$-dimensional Chern-Simons-like action, we also focus on the fermion sector to relate the $3+1$ dimensional extended massless QED to $2+1$-dimensional massive QED. We take advantage of this to state that the Chern-Simons-like action in extended massless QED can be induced with its coefficient being well defined and finite just as its $2+1$ counterpart. We make use of three different regularization schemes by inducting the Chern-Simons-like term in $3+1$ dimensions to support the conjecture.