Weaving commutators: beyond Fock space

TL;DR

This paper explores how quantum field theory in three-dimensional Einstein gravity involves deformed creation and annihilation operator algebras, suggesting potential implications for four-dimensional theories and the structure of multiparticle states.

Contribution

It introduces a deformed algebra framework for quantum fields coupled to 3D gravity, challenging traditional Fock space structures and symmetry actions.

Findings

Deformed algebra reflects non-trivial momentum space topology.

Modification of symmetry generator actions due to Newton's constant.

Qualitative implications for 4D quantum field theory structures.

Abstract

The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and are closely connected with the local properties of the fields and with the action of symmetry generators on observables and states. We here show that the quantum field theory describing relativistic particles coupled to three dimensional Einstein gravity as a topological defect must be constructed using a deformed algebra of creation and annihilation operators. This reflects a non-trivial group manifold structure of the classical momentum space and a modification of the Leibniz rule for the action of symmetry generators governed by Newton's constant. We outline various arguments suggesting that, at least at the qualitative level, these three-dimensional results could also apply to real four-dimensional world thus forcing us to re-think the ordinary multiparticle structure of quantum field theory and many of the fundamental aspects connected to it.