Loop expansion and the bosonic representation of loop quantum gravity

TL;DR

This paper introduces a new loop expansion in the bosonic representation of loop quantum gravity, enabling explicit semiclassical state expressions and efficient state projection onto physical constraints.

Contribution

It develops a novel loop expansion method within the bosonic formalism, facilitating state resolution and semiclassical analysis in loop quantum gravity.

Findings

Provides explicit loop expansions for coherent, heat kernel, and squeezed states.

Offers an efficient projection method onto physical state space.

Enhances semiclassical analysis capabilities in loop quantum gravity.

Abstract

We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent, heat kernel and squeezed states.