Quantum Fields as Category Algebras

TL;DR

This paper introduces a novel framework for quantum fields using category algebras and states, integrating relativity and quantum probabilistic structures within a unified categorical approach.

Contribution

It proposes defining quantum fields and states as category algebras on causal categories, directly incorporating relativity and noncommutative probability into quantum field theory.

Findings

Establishes a categorical formulation of quantum fields.

Connects the approach with AQFT and TQFT.

Provides a new perspective on quantum fields through category algebras.

Abstract

In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also discussed.