Extended Loops: A New Arena for Nonperturbative Quantum Gravity

TL;DR

This paper introduces an extended loop representation for gauge theories and quantum gravity, utilizing a Lie Group extension to better address regularization and solution finding in nonperturbative quantum gravity.

Contribution

It generalizes the loop representation with a Lie Group extension, enabling functional methods and new solutions to the Wheeler-DeWitt equation.

Findings

New solutions to the Wheeler-DeWitt equation

Reinforces the Jones Polynomial as a quantum gravity state

Provides a framework for regularization in loop quantum gravity

Abstract

We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension allows the use of functional methods to solve the constraint equations. It puts in a precise framework the regularization problems of the loop representation. It has practical advantages in the search for quantum states. We present new solutions to the Wheeler-DeWitt equation that reinforce the conjecture that the Jones Polynomial is a state of nonperturbative quantum gravity.