Symmetric vs. chiral approaches to massive fields with spin

TL;DR

This paper compares symmetric and chiral formulations of massive higher spin fields, showing their relation via invertible transformations, which aids in introducing interactions and controlling parity while maintaining Lorentz invariance.

Contribution

It establishes a connection between symmetric and chiral descriptions of massive higher spin fields through invertible variable changes, facilitating interaction development.

Findings

Chiral and symmetric approaches can be related via invertible transformations.

Chiral description avoids unphysical longitudinal modes.

Relation preserves Lorentz invariance and simplifies constraint handling.

Abstract

Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance.