Massless Limits of Massive Tensor Fields

TL;DR

This paper investigates gauge-fixing methods to achieve a smooth massless limit in massive tensor field theories, comparing Nakanishi's and BRS procedures on two models, with implications for nonlinear theory construction.

Contribution

It demonstrates that Nakanishi's gauge-fixing removes singularities in both models, while BRS regularizes only the ASG model, highlighting the BRS approach's potential for nonlinear theories.

Findings

Nakanishi's gauge-fixing eliminates massless singularities in both models.

BRS gauge-fixing regularizes the ASG model only.

BRS-regularized ASG model is promising for nonlinear theory development.

Abstract

In order to construct a massive tensor theory with a smooth massless limit, we apply two kinds of gauge-fixing procedures, Nakanishi's one and the BRS one, to two models of massive tensor field. The first is of the Fierz-Pauli (FP) type, which describes a pure massive tensor field; the other is of the additional-scalar-ghost (ASG) type, which includes a scalar ghost in addition to an ordinary tensor field. It is shown that Nakanishi's procedure can eliminate massless singularities in both two models, while the BRS procedure regularizes the ASG model only. The BRS-regularized ASG model is most promising in constructing a complete nonlinear theory.