Quantization of massive Abelian antisymmetric tensor field and linear potential

TL;DR

This paper explores the quantization of a massive Abelian antisymmetric tensor field, revealing how different gauges lead to a combined Yukawa and linear potential, advancing understanding of gauge theories with tensor fields.

Contribution

It provides a detailed comparison of covariant and axial gauge quantizations of the massive Abelian antisymmetric tensor field, connecting to Zwanziger's formulation and potential derivations.

Findings

Quantization in covariant gauge yields a generating functional with tensor current divergence.

Axial gauge quantization reproduces Zwanziger's formulation for electric and magnetic charges.

The resulting potential combines Yukawa and linear components.

Abstract

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an arbitrary gauge parameter and in the axial gauge of the Landau type. The covariant quantization yields the generating functional written in terms of an antisymmetric tensor current and its divergence. Origins of the terms in the generating functional are clearly understood in comparison with the quantization in the unitary gauge. The quantization in the axial gauge with a suitable axis directly yields the generating functional which is same as that obtained by using Zwanziger's formulation for electric and magnetic charges. It is shown that the generating functionals lead to a composite of the Yukawa and the linear potentials.