Duality for symmetric second rank tensors.(I): the massive case

TL;DR

This paper develops a Lagrangian-based method to construct dual descriptions for massive spin-two fields, generalizing duality transformations for Lorentz tensors and introducing a systematic scheme for duality construction.

Contribution

It introduces a purely Lagrangian approach using a first order parent Lagrangian to generate dual theories for massive spin-two fields, including interactions.

Findings

Constructed dual theories for massive spin-two fields

Developed a systematic scheme for duality transformations

Demonstrated duality for free and coupled Fierz-Pauli fields

Abstract

A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a systematic scheme for constructing the dual descriptions is developed. The method, a purely Lagrangian approach, is based on a first order parent Lagrangian, from which the dual partners are generated. In particular, a family of theories which are dual to the massive spin two Fierz-Pauli field, both free and coupled to an external source, is constructed in terms of a third rank tensor which is taken as the basic configuration variable.