Faraday lines and observables for the Einstein-Maxwell theory

TL;DR

This paper introduces an infinite set of gauge-invariant loop variables based on electric field lines for the Einstein-Maxwell theory, which could aid in quantization and analyzing classical solutions.

Contribution

It extends the loop variable approach from Einstein gravity to Einstein-Maxwell theory, providing a new framework for quantum and classical analysis.

Findings

Loop variables are invariant under spatial diffeomorphisms.

The loop variables form a closed Poisson algebra.

Potential usefulness for quantization and classical solutions.

Abstract

In recent work on Einstein gravity in four dimensions using the Ashtekar variables, non-local loop variables have played an important role in attempts to formulate a quantum theory. The introduction of such variables is guided by gauge invariance, and here an infinite set of loop variables is introduced for the Hamiltonian form of the Einstein-Maxwell theory. The loops that enter the description naturally are the (source free) electric field lines. These variables are invariant under spatial diffeomorphisms and they also form a closed Poisson algebra. As such they may be useful for quantization attempts and for studying classical solutions.