On the local Lorentz invariance in N=1 supergravity

TL;DR

This paper examines local Lorentz invariance in N=1 supergravity, correcting previous solutions and proposing a more general wave functional consistent with the Lorentz constraint.

Contribution

It provides an improved solution to the Lorentz constraint in N=1 supergravity using a new representation of Lorentz operators.

Findings

Corrected previous Lorentz constraint solutions

Developed a more general wave functional

Ensured compatibility with fermionic field representation

Abstract

We discuss the local Lorentz invariance in the context of N=1 supergravity and show that a previous attempt to find explicit solutions to the Lorentz constraint in terms of $\gamma-$matrices is not correct. We improve that solution by using a different representation of the Lorentz operators in terms of the generators of the rotation group, and show its compatibility with the matrix representation of the fermionic field. We find the most general wave functional that satisfies the Lorentz constraint in this representation.