Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

TL;DR

This paper develops a light-cone gauge framework to classify and derive cubic interaction vertices for arbitrary spin fermionic and bosonic fields, including massive and massless cases, in higher-dimensional flat space.

Contribution

It provides a complete classification of parity invariant cubic vertices for totally symmetric fields and explicit expressions for interactions like Yang-Mills and gravity involving massive arbitrary spin fields.

Findings

Derived restrictions on spins and derivatives for symmetric fields.

Classified all parity invariant cubic vertices for these fields.

Obtained explicit interaction expressions for Yang-Mills and gravity with massive spins.

Abstract

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang-Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.