Batalin-Tyutin Quantization of the Chern-Simons-Proca Theory

TL;DR

This paper applies the Batalin-Tyutin Hamiltonian method to quantize the Chern-Simons-Proca theory in three dimensions, revealing gauge invariance and new Wess-Zumino terms.

Contribution

It introduces a systematic embedding of second class constraints into first class constraints, producing gauge invariance and novel Wess-Zumino actions in the theory.

Findings

Derivation of St"uckelberg scalar term for anomaly cancellation

Identification of a new type of Wess-Zumino action

Establishment of gauge invariant Chern-Simons-Proca quantum theory

Abstract

We quantize the Chern-Simons-Proca theory in three dimensions by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second class constraint system into first class by introducing new fields in the extended phase space. As results, we obtain simultaneously the St\"uckelberg scalar term, which is needed to cancel the gauge anomaly due to the mass term, and the new type of Wess-Zumino action, which is irrelevant to the gauge symmetry. We also investigate the infrared property of the Chern-Simons-Proca theory by using the Batalin-Tyutin formalism comparing with the symplectic formalism. As a result, we observe that the resulting theory is precisely the gauge invariant Chern-Simons-Proca quantum mechanical version of this theory.