Quantum general invariance and loop gravity

TL;DR

This paper introduces a quantum projector for covariant theories, enabling the construction of spacetime operators in a loop quantum gravity framework, thus advancing the understanding of quantum general relativity.

Contribution

It proposes a novel quantum projector that retains gauge variables, facilitating the development of spacetime operators in a loop gravity approach.

Findings

A quantum projector for covariant theories is formulated.

Spacetime area and volume operators are constructed.

The approach maintains gauge variables in the quantum formalism.

Abstract

A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge symmetry transformations which are connected to the identity. Gauge variables are retained in this formalism, thus permitting the construction of spacetime area and volume operators in a tentative spacetime loop formulation of quantum general relativity.