Covariant Effective Action for Antisymmetric Tensor Field

TL;DR

This paper develops a covariant quantization method for rank-2 antisymmetric tensor fields, addressing gauge symmetry complexities, and applies it to a massive case, confirming previous results.

Contribution

It generalizes the DeWitt-Vilkovisky formalism to handle additional gauge symmetries in antisymmetric tensor fields.

Findings

Successfully quantized a massive rank-2 antisymmetric field

Reproduced known results using the covariant effective action approach

Provided a geometrical understanding of gauge symmetry complexities

Abstract

Covariant quantization of rank-2 antisymmetric fields is non-trivial due to additional symmetries of the gauge parameters. We present an intuitive way to deal with this additional symmetry of gauge parameters in terms of geometrical understanding of field space. We generalize the DeWitt-Vilkovisky covariant effective action formalism for quantization of such theories. As an application, we quantize a massive rank-2 antisymmetric field using the covariant effective action approach and reproduce previously obtained results.