Causal Network Condensation

TL;DR

This paper introduces a novel framework called causal network condensation, generalizing topological quantum field theories using categorical and diagrammatic methods, unifying spin networks, Turaev-Viro models, and causal set theory.

Contribution

It presents new categorical concepts and a nerve functor that extend existing topological quantum field theory constructions.

Findings

Defines causal network category and diagrams.

Introduces gauge transformations for these diagrams.

Develops a nerve functor generalizing simplicial categories.

Abstract

In this paper, we introduce a generalized topological quantum field theory based on the symmetric monoidal category which we call causal network condensation since it can be regarded as a generalization of spin network construction of Baez, Turaev-Viro model and causal set theory. In this paper we introduce some new concepts, including causal network category, causal network diagrams, and their gauge transformations. Based on these concepts, we introduce the nerve functor for the symmetric monoidal category. It can be regarded as a generalization of the nerve functor for simplicial category.