Unique Deformation of Local Quantum Field Theory Resulting in Divergence-free Amplitudes

TL;DR

This paper introduces a novel deformation of local quantum field theory using a *-product, resulting in a divergence-free framework that incorporates a fundamental length scale, addressing longstanding issues with infinities.

Contribution

It presents an essentially unique deformation of quantum fields at a point, proposing a divergence-free theory with a fundamental length, expanding on Faddeev's previous deformations.

Findings

The deformation leads to divergence-free amplitudes.

The theory incorporates a fundamental length scale.

It offers a new approach to quantum field theory without divergences.

Abstract

An essentially unique deformation of the product of quantum fields at the same spacetime point is obtained. It is proposed to replace local quantum field theory with another structure which uses a *-product. The resulting theory contains a fundamental length and is free from divergences. This provides the third deformation suggested by Faddeev.