Symplectic quantization of self-dual master Lagrangian

TL;DR

This paper applies symplectic and Dirac quantization methods to the master Lagrangian connecting self-dual and Maxwell-Chern-Simons theories, demonstrating their equivalence and extending the system to gauge symmetry.

Contribution

It compares symplectic and Dirac quantization of the master Lagrangian and constructs an extended gauge-invariant system within both frameworks.

Findings

Symplectic and Dirac procedures are equivalent for the system.

An extended first-class gauge system is successfully constructed.

The gauge generator is explicitly derived in both approaches.

Abstract

We consider the master Lagrangian of Deser and Jackiw, interpolating between the self-dual and the Maxwell-Chern-Simons Lagrangian, and quantize it following the symplectic approach, as well as the traditional Dirac scheme. We demonstrate the equivalence of these procedures in the subspace of the second-class constraints. We then proceed to embed this mixed first- and second-class system into an extended first-class system within the framework of both approaches, and construct the corresponding generator for this extended gauge symmetry in both formulations.