Exploring the second class constraint quantization approach proposed by Batalin and Marnelius

TL;DR

This paper extends the Batalin-Marnelius second class constraint quantization method, analyzing its relation to other approaches, defining a compatible bracket, and applying it to systems with mixed constraints and simple examples.

Contribution

It introduces an extension of the second class constraint quantization method to mixed systems and develops a compatible bracket for operator formalism.

Findings

The method is successfully extended to mixed class constraints.

A new bracket compatible with the operator formalism is defined.

Applications to simple example systems demonstrate the approach.

Abstract

I extend upon the paper by Batalin and Marnelius, in which they show how to construct and quantize a gauge theory from a Hamiltonian system with second class constraints. Among the avenues explored, their technique is analyzed in relation to other well-known methods of quantization and a bracket is defined, such that the operator formalism can be fully developed. I also extend to systems with mixed class constraints and look at some simple examples.