Cubic interaction vertices for massive and massless higher spin fields

TL;DR

This paper develops methods using light-cone formalism to construct and classify cubic interaction vertices for massive and massless higher spin fields in flat space, providing explicit formulas and restrictions.

Contribution

It introduces new techniques for constructing and classifying cubic interaction vertices for higher spin fields in flat space, including explicit formulas and restrictions.

Findings

Derived restrictions on spins and derivatives for cubic vertices.

Obtained explicit interaction vertices for massive and massless higher spins.

Classified parity invariant and violating vertices in 5 and 6 dimensions.

Abstract

Using the light-cone formulation of relativistic dynamics, we develop various methods for constructing cubic interaction vertices and apply these methods to the study of higher spin fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for massive and massless higher spin fields of arbitrary symmetry are obtained. We derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for totally symmetric fields. As an example of application of the light-cone formalism, we obtain simple expressions for the minimal Yang-Mills and gravitational interactions of massive totally symmetric arbitrary spin fields. We give the complete list of parity invariant and parity violating cubic interaction vertices that can be constructed for massless fields in five and six-dimensional spaces.