Polymer and Fock representations for a Scalar field

Details Polymer and Fock representations for a Scalar field Polymer and Fock representations for a Scalar field

2002-11-04

arxiv.org/abs/gr-qc/0211012v1

Class.Quant.Grav. 20 (2003) L11-1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, no figures

Scientific paper

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.

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