BRST quantization of vector and axial-vector gauge theory

Abstract

The vector and axial-vector gauge theory is quantized in the geometrical BRST formalism. By applying the so-called horizontality condition, the BRST and anti-BRST transformation rules under the vector and axial-vector gauge transformations are obtained. At the same time, a quantum Lagrangian which is BRST and anti-BRST invariant is obtained. We discuss how the vector-axial-vector gauge theory [${\mathrm{U}}_{V}(N)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{A}(N)$] is related to the "right-" and "left"-handed gauge theory [${\mathrm{U}}_{R}(N)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{L}(N)$].