Higher spin fields with reversed spin-statistics relation

TL;DR

This paper introduces a method to construct massive fields with arbitrary spin that have reversed spin-statistics relations, by doubling Lorentz group representations, enabling new commutation properties while preserving particle spin.

Contribution

The paper presents a novel construction of higher spin fields with reversed spin-statistics relation using doubled Lorentz representations, linking them to normal fields for easier analysis.

Findings

Reversed spin-statistics fields can be expressed in terms of normal fields.

The construction applies to scalar and Dirac fields.

It enables defining opposite commutation properties for these fields.

Abstract

A construction of massive free fields with arbitrary spin and reversed spin-statistics relation is presented. The main idea of the construction is to consider fields that transform according to representations of the Lorentz group that are doubled in comparison with the representations according to which normal (physical) fields transform. This allows the definition of opposite commutation properties for these fields, while the spin of the particles they describe remains unchanged. The correspondence established by the construction between fields obeying normal and reversed spin-statistics relation makes it possible to express e.g. the polarization states, (anti)commutators, or Feynman propagators of the latter fields in terms of those of the normal fields to which they correspond. The cases of the scalar and Dirac fields are discussed in additional detail.