Models of Quantum Space Time: Quantum Field Planes

TL;DR

This paper introduces quantum field planes as a noncommutative differential algebra derived from quantum field theory, replacing classical function algebras with noncommutative observables.

Contribution

It presents a novel framework for modeling quantum space-time using noncommutative differential algebra based on quantum field theory data.

Findings

Constructs a noncommutative differential algebra from quantum field theory

Replaces classical function algebras with noncommutative observable algebras

Provides a new mathematical model for quantum space-time

Abstract

Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field theory. The basic idea is to replace the ground field ${\bf C}$ of quantum planes by the noncommutative algebra ${\cal A}$ of observables of the quantum field theory.