On Dual Formulations of Massive Tensor Fields

TL;DR

This paper develops a gauge-invariant approach to dual formulations of massive tensor fields, resolving ambiguities in traditional methods and illustrating the approach with examples involving spin-2 fields in various spacetime backgrounds.

Contribution

It introduces a gauge-invariant method for constructing dual formulations of massive tensor fields applicable in Minkowski and (Anti) de Sitter spaces, addressing previous ambiguities.

Findings

Successfully applied to spin-2 fields in different backgrounds

Provides a consistent dual formulation framework

Resolves ambiguity in first order parent Lagrangian methods

Abstract

In this paper we investigate dual formulations for massive tensor fields. Usual procedure for construction of such dual formulations based on the use of first order parent Lagrangians in many cases turns out to be ambiguous. We propose to solve such ambiguity by using gauge invariant description of massive fields which works both in Minkowski space as well as (Anti) de Sitter spaces. We illustrate our method by two concrete examples: spin-2 "tetrad" field h_{\mu a}, the dual field being "Lorentz connection" \omega_{\mu,ab} and "Riemann" tensor R_{\mu\nu,ab} with the dual \Sigma_{\mu\nu,abc}.