Quantum Einstein-Maxwell Fields: A Unified Viewpoint from the Loop Representation

TL;DR

This paper introduces a unified approach to electromagnetism and gravity using loop quantum gravity techniques, revealing new connections with topological invariants like the Jones Polynomial.

Contribution

It extends Ashtekar's variables to unify electromagnetic and gravitational fields within the loop representation framework.

Findings

Wavefunctions depend on two loops encoding both fields

Chern-Simons form and Jones Polynomial are relevant in the model

Proposes a new perspective on unifying fundamental interactions

Abstract

We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wavefunctions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simons form and the Jones Polynomial play a role in the model.