Quantization of discretized spacetimes and the correspondence principle

TL;DR

This paper proposes an algebraic quantization method for discretized spacetime models, linking finite structures to continuous manifolds through a limiting process interpreted as a correspondence principle.

Contribution

It introduces a novel algebraic quantization framework for discretized spacetimes and interprets the continuum limit as a quantum correspondence principle.

Findings

Establishes a duality between finitary substitutes and incidence algebras.

Provides a limiting procedure connecting discrete models to classical spacetime.

Interprets the continuum limit within an algebraic quantum framework.

Abstract

An algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras. The provided limiting procedure that yields conventional manifold characteristics of spacetime structures is interpreted in the algebraic quantum framework as a correspondence principle.