Spin one matter fields

TL;DR

This paper develops a formalism for describing massive spin-one matter fields in the ormalism, analyzing their properties, constraints, and interactions, and concludes they cannot have chiral gauge interactions but can have vector gauge interactions.

Contribution

It introduces a covariant projection-based formalism for massive spin-one fields in the ormalism, enabling constraint solving and canonical quantization, and classifies their renormalizable self-interactions.

Findings

The theory is not chirally symmetric in the massless limit.

Spin-one matter fields can have vector gauge interactions.

Self-interactions are naively renormalizable based on field dimension.

Abstract

Spin-one matter fields are relevant both for the description of hadronic states and as potential extensions of the Standard Model. In this work we present a formalism for the description of massive spin-one fields transforming in the $(1,0)\oplus(0,1)$ representation of the Lorentz group, based on the covariant projection onto parity eigenspaces and Poincar\'e orbits. The formalism yields a constrained dynamics. We solve the constraints and perform the canonical quantization accordingly. This formulation uses the recent construction of a parity-based covariant basis for matrix operators acting on the $(j,0)\oplus(0,j) $ representations. The algebraic properties of the covariant basis play an important role in solving the constraints and allowing the canonical quantization of the theory. We study the chiral structure of the theory and conclude that it is not chirally symmetric in the massless limit, hence it is not possible to have chiral gauge interactions. However, spin-one matter fields can have vector gauge interactions. Also, the dimension of the field makes self-interactions naively renormalizable. Using the covariant basis, we classify all possible naively renormalizable self-interaction terms.