On Path Integration on Noncommutative Geometries

TL;DR

This paper explores a quantum field theory path integral approach on noncommutative geometries that regularize UV/IR divergences, focusing on momentum spaces over curved geometries and their commutation relations.

Contribution

It provides a coordinate-free formulation of commutation relations for noncommutative geometries arising as momentum spaces over curved spaces.

Findings

Derived full set of commutation relations using Synge world function

Demonstrated UV/IR regularization in noncommutative geometries

Established a coordinate-free framework for these geometries

Abstract

We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries arise as `momentum spaces' over curved spaces, for which we can now give the full set of commutation relations in coordinate free form, based on the Synge world function.