Gravitational dressing: from the crossed product to more general algebraic and mathematical structure

TL;DR

This paper explores how gravitational dressing constructions relate to algebraic structures in quantum gravity, revealing a transition from von Neumann algebras of type III to II and suggesting a broader mathematical framework.

Contribution

It extends standard gravitational dressing constructions to more general algebraic structures, connecting the crossed product to a wider mathematical context in quantum gravity.

Findings

Transition from type III to II algebras via gravitational dressing

Identification of noncommutative structures in separated regions

Potential explanation of holographic behavior for gravity

Abstract

The crossed product, and consequent transition from von Neumann algebras of type III to II, is recovered from a truncation of more general gravitational dressing constructions, about certain spacetimes. This is done by extending "standard dressing" constructions previously used to give a perturbative definition of "gravitational splittings," defining approximate localization of information. This result appears to illustrate that this algebraic transition is a small piece of a more general algebraic, or other mathematical, structure associated with quantum gravity. The leading-order structure involves noncommutativity from separated regions, and at the nonperturbative level connects with a possible explanation of holographic behavior for gravity.