Cubic interaction vertices for massive/massless continuous-spin fields and arbitrary spin fields

TL;DR

This paper develops a formalism to construct and classify cubic interaction vertices involving massive, massless, and continuous-spin fields in flat space, providing a comprehensive list of such interactions.

Contribution

It introduces a systematic method to derive all parity-invariant cubic vertices for continuous-spin and arbitrary spin fields, expanding the understanding of their interactions.

Findings

Derived parity-invariant cubic vertices for mixed continuous-spin and arbitrary spin fields

Classified all cubic interaction vertices for continuous-spin fields in flat space

Provided explicit forms for self-interacting continuous-spin field vertices

Abstract

We use light-cone gauge formalism to study interacting massive and massless continuous-spin fields and finite component arbitrary spin fields propagating in the flat space. Cubic interaction vertices for such fields are considered. We obtain parity invariant cubic vertices for coupling of one continuous-spin field to two arbitrary spin fields and cubic vertices for coupling of two continuous-spin fields to one arbitrary spin field. Parity invariant cubic vertices for self-interacting massive/massless continuous-spin fields are also obtained. We find the complete list of parity invariant cubic vertices for continuous-spin fields and arbitrary spin fields.