On Finite 4D Quantum Field Theory in Non-Commutative Geometry

TL;DR

This paper constructs a finite 4D quantum field theory on a non-commutative sphere, maintaining symmetry and avoiding typical UV divergences, offering a novel approach to quantum field models.

Contribution

It introduces a finite 4D scalar field theory on a non-commutative sphere with preserved SO(5) symmetry and no UV divergences, advancing non-commutative geometry applications.

Findings

Finite 4D scalar field theory constructed on non-commutative sphere

UV divergences are absent in the model

Symmetry is preserved during quantization

Abstract

The truncated 4-dimensional sphere $S^4$ and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the finite number of degrees of freedom. The usual field theory UV-divergences are manifestly absent.