Free Fields for Any Spin in 1+2 Dimensions

TL;DR

This paper constructs free quantum fields of any spin in 1+2 dimensions by analyzing Poincaré group representations and applying Weinberg's method, with insights into axiomatic field theory in this setting.

Contribution

It introduces a systematic construction of free fields of arbitrary spin in 1+2 dimensions using fiber bundle formalism and Weinberg's approach.

Findings

Explicit construction of arbitrary spin free fields in 1+2 dimensions

Detailed analysis of Poincaré group representations in this context

Comments on axiomatic field theory in 1+2 dimensions

Abstract

We construct free fields of arbitrary spin in 1+2 dimensions i.e. free fields for which the one-particle Hilbert space carries a projective isometric irreducible representation of the Poincar\'e group in 1+2 dimensions. We analyse in detail these representations in the fiber bundle formalism and afterwards we apply Weinberg procedure to construct the free fields. Some comments concerning axiomatic field theory in 1+2 dimensions are also made.