Photons from quantized electric flux representations

TL;DR

This paper explores the relationship between polymer-like quantum states of electric flux in loop quantum gravity and wave-like photon states in Fock space, providing insights into how gravitons may emerge from non-perturbative quantum gravity frameworks.

Contribution

It establishes a connection between the electric flux representation and the Fock representation, showing how wave-like photons relate to polymer-like states in loop quantum gravity.

Findings

Normalizable Fock states correspond to distributional states in the flux representation.

The work clarifies the emergence of photon-like excitations from quantum geometric states.

Provides a framework for understanding gravitons in loop quantum gravity.

Abstract

The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in loop quantum gravity. We investigate the relation between this representation, in which the basic excitations are `polymer-like', and the Fock representation, in which the basic excitations are wave-like photons. We show that normalizable states in the Fock space are associated with `distributional' states in the quantized electric flux representation. This work is motivated by the question of how wave-like gravitons in linearised gravity arise from polymer-like states in non-perturbative loop quantum gravity.