Hamiltonian Formulation of Jackiw--Pi 3-Dimensional Gauge Theories

TL;DR

This paper analyzes the Hamiltonian structure of Jackiw-Pi 3D gauge theories, addressing gauge symmetry issues and proposing modifications to improve quantization while preserving physical degrees of freedom.

Contribution

It provides a Hamiltonian formulation of Jackiw-Pi theories, clarifies gauge symmetry and degrees of freedom, and suggests a modification to constraints to facilitate quantization.

Findings

All theories share the same physical degrees of freedom.

Quadratic action has more gauge symmetries than the original.

Proposed constraint modification aims to improve perturbation expansion.

Abstract

A 3-dimensional non-abelian gauge theory was proposed by Jackiw and Pi to create mass for the gauge fields. However, the quadratic action obtained by switching off the non-abelian interactions possesses more gauge symmetries than the original one, causing some difficulties in quantization. Jackiw and Pi proposed another action by introducing new fields, whose gauge symmetries are consistent with the quadratic part. It is shown that all of these theories have the same number of physical degrees of freedom in the hamiltonian framework. Hence, as far as the physical states are considered there is no inconsistency. Nevertheless, perturbation expansion is still problematic. To cure this we propose to modify one of the constraints of the non-abelian theory without altering neither its canonical hamiltonian nor the number of physical states.