A Uniqueness Theorem and Its Application to Field-Theoretical Models with a Fundamental Length

TL;DR

This paper proves a mathematical uniqueness theorem for distributions with exponential growth and applies it to quasi-local quantum field theories, showing that many local QFT predictions remain valid even with a fundamental length scale.

Contribution

It introduces a new uniqueness theorem for distributions supported in convex cones and applies it to establish the persistence of local QFT properties in theories with a fundamental length.

Findings

Theorem constrains distributions with exponential growth and support in convex cones.

Many local QFT predictions hold in theories with a fundamental length.

Supports the consistency of string theory-inspired models with established QFT results.

Abstract

It is shown that if a distribution V of exponential growth has support in a proper convex cone and its Fourier transform is carried by a closed cone different from whole space, then V=0. The application of this result to a {\em quasi-local} quantum field theory (where the fields are localizable only in regions greater than a certain scale of nonlocality) is contemplated. In particular, we show that a number of physically important predictions of {\em local} quantum field theory also hold in a quantum field theory with a fundamental length, as indicated from string theory.