Space of quantum states built over metrics of fixed signature

TL;DR

This paper develops a diffeomorphism-invariant framework for quantum states and observables built over all metrics with a fixed signature on a manifold, providing a new geometric approach to quantum theory.

Contribution

It introduces a novel construction of quantum state space and algebra over metrics of fixed signature, invariant under diffeomorphisms, with uniqueness up to natural isomorphisms.

Findings

Constructed a space of quantum states over fixed signature metrics

Defined an algebra of quantum observables compatible with the state space

Ensured the construction's invariance under diffeomorphisms

Abstract

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural isomorphisms.