A Theory of algebraic integration

TL;DR

This paper develops a theoretical framework for defining integrals over nonclassical configuration spaces in quantum theories, ensuring composition of probability amplitudes for a broad class of algebras.

Contribution

It introduces a novel algebraic integration method that addresses the quantization of theories on nonclassical spaces, extending the path-integral approach.

Findings

Defined an algebraic integration respecting composition principles

Applicable to a large class of algebras in quantum theories

Provides a foundation for quantization over nonclassical configuration spaces

Abstract

In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such spaces. We consider this problem and we show how to define an integration which respects the physical principle of composition of the probability amplitudes for a very large class of algebras.