A mathematical bridge between discretized gauge theories in quantum physics and approximate reasoning in pairwise comparisons

TL;DR

This paper establishes a mathematical connection between discretized gauge theories in quantum physics and pairwise comparison methods in information theory, using the concept of holonomy along simplices, opening new research questions.

Contribution

It introduces a novel mathematical link between gauge theories and pairwise comparisons through holonomy, bridging physics and information theory.

Findings

Identifies a correspondence via holonomy in simplices.

Raises open questions in both gauge theories and pairwise comparisons.

Provides a new perspective for interdisciplinary research.

Abstract

We describe a mathematical link between aspects of information theory, called pairwise comparisons, and discretized gauge theories. The link is made by the notion of holonomy along the edges of a simplex. This correspondance leads to open questions in both field.