Cubic interactions of arbitrary spin fields in 3d flat space

TL;DR

This paper classifies and explicitly constructs all cubic interaction vertices for arbitrary spin fields in 3D flat space using light-cone gauge, covering both massive and massless cases with first-derivative and higher-derivative forms.

Contribution

It provides a comprehensive classification and explicit expressions for cubic interactions of arbitrary spin fields in 3D flat space, including both massive and massless cases.

Findings

Explicit cubic interaction vertices for all spins are derived.

Two forms of vertices are studied: first-derivative and higher-derivative.

All vertices are constructed using the first-derivative form.

Abstract

Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and one-half spin) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic interaction vertices which we refer to as first-derivative form and higher-derivative form. All cubic interaction vertices are built by using the first-derivative form.