Space-time dynamics from algebra representations

TL;DR

This paper introduces a novel model for space-time dynamics using algebraic representations, potentially serving as a framework for 2-D quantum gravity by embedding Lie algebra structures into a larger algebra that encodes space-time evolution.

Contribution

It develops a new algebraic approach to incorporate dynamics into space-time geometry via C*-algebras and Lie algebra representations, linking different space-times.

Findings

Constructs a space-time model from a C*-algebra based on Lie algebra generators.

Introduces a larger algebra that mixes representations to generate dynamics.

Proposes a potential framework for 2-D quantum gravity.

Abstract

We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie algebra G. This algebra is included as a subalgebra in a bigger algebra F, the generators of which mix the representations of G in a way that relates different space-times and creates the dynamics. This construction can be considered eventually as a model for 2-D quantum gravity.