Homotopy approach to quantum gravity

TL;DR

This paper introduces a novel finite-dimensional quantum gravity theory using a homotopy approach, where the quantum history involves multiple fermionic levels and the diffeomorphism group emerges as a limit, with algebraic and multivector structures.

Contribution

It presents a new homotopy-based method to construct a finite-dimensional quantum gravity theory with unique algebraic and geometric features.

Findings

Quantum history includes multiple fermionic levels

Diffeomorphism group appears as a singular limit

Gravitational form is represented by algebraic square

Abstract

I construct a finite-dimensional quantum theory from general relativity by a homotopy method. Its quantum history is made up of at least two levels of fermionic elements. Its unitary group has the diffeomorphism group as singular limit. Its gravitational metrical form is the algebraic square. Its spinors are multivectors.