Bv Quantization of a Vector-Tensor Gauge Theory With Topological Coupling

Abstract

We use the BV quantization method for a theory with coupled tensor and vector gauge fields through a topological term. We consider in details the reducibility of the tensorial sector as well as the appearance of a mass term in the effective vectorial theory .

Mass generation for gauge fields in the Salam-Weinberg theory without Higgs bosons

“…Classically, if one eliminates j I and j? I by using their equation of motion, the mass terms M¼ ?I ¼?I and MB I BI will be obtained, the same occurs in the quantum point of view, when tensor gauge fields are introduced [3]. Let us work classically first.…”

“…I and d? I are related to the ones of tensor fields and d and d are the ghosts related to the reducibility condition (see [3] for details). Integrating over the tensor fields, we obtain…”

Axial and gauge anomalies in a theory with one and two-form gauge fields

“…The case where vector and tensor fields are topologically coupled was considered in [4]. The inclusion of fermions induces only simple modifications regarding the results found in [4]. We get for the field-antifield action…”

“…The case involving only tensor fields can be found in References [9,13]. The case where vector and tensor fields are topologically coupled was considered in [4]. The inclusion of fermions induces only simple modifications regarding the results found in [4].…”

“…If now we integrate out the tensor degrees of freedom, it is not difficult to see that the effective action obtained in [4] is generalized tō…”