Extended diffeomorphism algebras in (quantum) gravitational physics

TL;DR

This paper develops an explicit mathematical representation of local diffeomorphism algebras in manifold-based gravitational models, connecting abstract algebraic structures with physical gravitational concepts.

Contribution

It introduces a general formalism for representing diffeomorphism algebras in quantum gravity, adaptable to various gravitational models.

Findings

Constructed explicit algebra representations for manifolds with realistic dimensions.

Linked algebraic structures to physical gravitational notions.

Outlined multiple strategies for model development.

Abstract

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is characterized by the fundamental role assigned to a basic underlying symmetry. The developed mathematical formalism makes contact with the relevant gravitational notions by means of the addition of some extra structure. The specific manners in which this is accomplished, together with their corresponding physical interpretation, lead to different gravitational models. Distinct strategies are in fact briefly outlined, showing the versatility of the present conceptual framework.