Quantization of diffeomorphism invariant theories of connections with a non-compact structure group - an example

TL;DR

This paper demonstrates the quantization of a diffeomorphism invariant connection theory with a non-compact group, using Loop Quantum Gravity techniques and projective methods, providing a concrete example with R as the structure group.

Contribution

It introduces a novel quantization of a non-compact group connection theory, extending Loop Quantum Gravity methods to new settings with R as the structure group.

Findings

Quantum states constructed via projective techniques

Quantization closely resembles self-dual Plebanski action

Framework extends LQG methods to non-compact groups

Abstract

A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a four-dimensional 'space-time' by an action resembling closely the self-dual Plebanski action for general relativity. The space of quantum states is constructed by means of projective techniques by Kijowski. Except this point the applied quantization procedure is based on Loop Quantum Gravity methods.