A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions

TL;DR

This paper introduces a renormalizable massive Abelian gauge theory in 2+1 dimensions using a Chern-Simons kinetic term and Stuekelberg mass, demonstrating its renormalizability and analyzing its quantum properties.

Contribution

It proposes a novel 2+1D Abelian gauge model with a Chern-Simons kinetic term and Stuekelberg mass, showing its renormalizability and quantum behavior up to two loops.

Findings

One-loop spinor self energy computed using operator regularization.

Two-loop vector self energy vanishes, indicating zero beta function.

The model's canonical structure is analyzed via Dirac constraint formalism.

Abstract

The standard formulation of a massive Abelian vector field in $2+1$ dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to super renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self energy is computed using operator regularization, a technique which respects the three dimensional character of the antisymmetric tensor $\epsilon_{\alpha\beta\gamma}$. This method is used to evaluate the vector self energy to two-loop order; it is found to vanish showing that the beta function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.