Towards Finite Quantum Field Theory in Non-Commutative Geometry

TL;DR

This paper demonstrates that a self-interacting scalar field on a truncated sphere can be quantized using path integrals, resulting in a finite theory with automatic UV-regularization due to symmetry properties.

Contribution

It introduces a finite quantum scalar field model on a non-commutative geometry with automatic UV-regularization, advancing quantum field theory in curved spaces.

Findings

The model is finite and UV-regularized automatically.

The scalar field respects sphere isometries.

Quantization is achieved via path integral approach.

Abstract

We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We explicitely show that the model is finite and the UV-regularization automatically takes place.