Polymer and Fock representations for a Scalar field

TL;DR

This paper develops a background-independent framework for scalar matter fields in loop quantum gravity, connecting polymer and Fock representations to bridge quantum geometry with low-energy physics.

Contribution

It constructs the polymer and Fock representations for scalar fields within loop quantum gravity, addressing previous gaps in the scalar sector.

Findings

Established polymer representation for scalar fields.

Connected polymer and Fock representations for scalar matter.

Enhanced the understanding of matter coupling in background-independent quantum gravity.

Abstract

In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.