Consistent interactions and involution

TL;DR

This paper introduces a universal, covariant method for constructing consistent interactions between fields, applicable to various types of equations and constraints without auxiliary fields.

Contribution

It presents a new, general approach to identify all consistent interactions in field theories, regardless of gauge symmetry or Hamiltonian structure.

Findings

Method applies to Lagrangian and non-Lagrangian equations.

Identifies all consistent interactions without auxiliary fields.

Works with theories having gauge symmetry or second class constraints.

Abstract

Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is explicitly covariant. No auxiliary fields are introduced. The equations may have (or have no) gauge symmetry and/or second class constraints in Hamiltonian formalism, providing the theory admits a Hamiltonian description. In every case the method identifies all the consistent interactions.