Quantum field theory with a preferred direction: The very special relativity framework

TL;DR

This paper constructs a quantum field theory within the very special relativity framework, incorporating a preferred direction, and analyzes its implications on particle behavior and interactions.

Contribution

It provides a rigorous construction of quantum fields with a preferred direction based on the VSR group, extending to higher spins and analyzing interaction effects.

Findings

Particles differ between VSR and Lorentz sectors but share similarities.

Massive spin-half and spin-one fields are local and obey Dirac and Proca equations.

Preferred direction affects polarized processes but not unpolarized ones.

Abstract

The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group $ISIM(2)$, we present a rigorous construction of quantum field theory with a preferred direction. We find, although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations respectively. This result can be generalised to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarised processes but are otherwise absent.