Massive Supersymmetric Quantum Gauge Theory

TL;DR

This paper develops a quantum framework for massive supersymmetric gauge theories, constructing the physical Hilbert space, ensuring gauge invariance, and deriving an interacting Lagrangian with doubled ghost fields, advancing the understanding of supersymmetric quantum gauge models.

Contribution

It introduces a quantum construction of the supersymmetric vector multiplet, including the physical Hilbert space and gauge-invariant couplings, with novel ghost field structure.

Findings

Constructed the physical Hilbert space considering gauge structure.

Established gauge invariance of the supersymmetric coupling in first-order perturbation.

Derived a massive Yang-Mills Lagrangian with doubled ghost fields.

Abstract

We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-dimensional physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.