On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

TL;DR

This paper explores quantum field theories on noncommutative spaces with minimal uncertainties in positions and momenta, demonstrating regularization of divergences in a specific scalar field theory model.

Contribution

It extends previous work by analyzing noncommutative geometries that introduce minimal uncertainties, including those inspired by string theory and quantum gravity, and shows their effect on field theory regularization.

Findings

Ultraviolet and infrared regularization of all graphs in the studied model

Implementation of minimal uncertainties in positions and momenta

Application to euclidean φ^4-theory

Abstract

We continue studies on quantum field theories on noncommutative geometric spaces, focusing on classes of noncommutative geometries which imply ultraviolet and infrared modifications in the form of nonzero minimal uncertainties in positions and momenta. The case of the ultraviolet modified uncertainty relation which has appeared from string theory and quantum gravity is covered. The example of euclidean $\phi^4$-theory is studied in detail and in this example we can now show ultraviolet and infrared regularisation of all graphs.