Derivation of All Symmetries from First Class Constraints and Quantization in 2+1 Dimensional Supergravity

TL;DR

This paper derives gauge symmetries from first class constraints in 2+1 dimensional N=1 supergravity, demonstrating algebra closure and performing quantization with mixed Bosonic and Fermionic ghosts.

Contribution

It constructs a generator of all gauge symmetries from first class constraints and applies it to quantize 2+1D supergravity, including ghost analysis.

Findings

Gauge symmetry generator derived from constraints

Symmetry algebra shown to close

Quantization includes mixed Bosonic and Fermionic ghosts

Abstract

The first class constraints in N = 1 supergravity in 2 + 1 dimensions are used to construct a generator of three gauge symmetries (including a local supersymmetry) that leave the action invariant. The algebra of these symmetries closes. This generator is used to quantize the model; a ghost involving both Bosonic and Fermionic components arises.