Non-closure of constraint algebra in N=1 supergravity

TL;DR

This paper investigates the constraint algebra in N=1 supergravity, revealing that it does not close formally under certain operator orderings, which impacts the canonical quantization process.

Contribution

It demonstrates the non-closure of the constraint algebra in N=1 supergravity using the holomorphic action and specific operator orderings.

Findings

The algebra's structure functions are explicitly given.

The algebra fails to close formally for two operator orderings.

Implications for canonical quantization of supergravity are discussed.

Abstract

The algebra of constraints arising in the canonical quantization of N=1 supergravity in four dimensions is investigated. Using the holomorphic action, the structure functions of the algebra are given and it is shown that the algebra does not close formally for two chosen operator orderings.