Two roads to noncommutative causality

TL;DR

This paper reviews two approaches to noncommutative causality, comparing their mathematical frameworks and physical motivations using a specific Minkowski space example.

Contribution

It provides a comparative analysis of isocone-based and Lorentzian spectral triple frameworks for noncommutative causality.

Findings

Both frameworks are applied to the Minkowski plane with finite noncommutative space.

The paper highlights similarities and differences between the two approaches.

It clarifies the mathematical structures underlying noncommutative causality.

Abstract

We review the physical motivations and the mathematical results obtained so far in the isocone-based approach to noncommutative causality. We also give a briefer account of the alternative framework of Franco and Eckstein which is based on Lorentzian spectral triples. We compare the two theories on the simple example of the product geometry of the Minkowski plane by the finite noncommutative space with algebra $M_2({\mathbb C})$.