The Lorentzian distance formula in noncommutative geometry

TL;DR

This paper reviews the development of a Lorentzian distance formula within noncommutative geometry, consolidating previous efforts into a coherent framework for future research.

Contribution

It provides a comprehensive historical overview and synthesis of the key steps in formulating a Lorentzian distance in noncommutative geometry.

Findings

Consolidation of prior research milestones

Clarification of the Lorentzian distance construction

Foundation for future applications in noncommutative geometry

Abstract

For almost twenty years, a search for a Lorentzian version of the well-known Connes' distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put those elements together in order to get a valid and functional formula. This paper presents a historical review of the construction and the proof of a Lorentzian distance formula suitable for noncommutative geometry.