Matter Fields in Curved Space-Time

TL;DR

This paper explores the geometric structure of a two-sheeted space-time using non-commutative geometry, aiming to model chiral fields and their interactions in curved space-time as a step towards understanding the Standard Model in such a setting.

Contribution

It introduces a novel two-sheeted space-time model within non-commutative geometry to describe chiral fields and their interactions in curved space-time.

Findings

Constructed a model of left- and right-chiral fields on two-sheeted space-time.

Developed action functionals for interactions of these chiral fields.

Provides groundwork for incorporating the Standard Model in curved space-time.

Abstract

We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions.