BFT Method for Mixed Constrained Systems and Chern-Simons Theory

TL;DR

This paper examines the limitations of the BFT embedding method for mixed constrained systems, using Chern-Simons theory as a case study, and proposes two solutions to improve the method.

Contribution

It identifies issues with BFT embedding in mixed systems and introduces two novel approaches to achieve finite order embeddings for Chern-Simons theory.

Findings

BFT method is problematic for mixed systems.

Two new methods successfully embed Chern-Simons theory.

Different finite order embeddings are achieved with each method.

Abstract

We show that the BFT embedding method is problematic for mixed systems (systems possessing both first and second class constraints). The Chern-Simons theory as an example is worked out in detail. We give two methods to solve the problem leading to two different types of finite order BFT embedding for Chern-Simons theory.