The Product Arbitrariness of Generalised Functions and its Role in Quantum Field Theory

TL;DR

This paper investigates the product arbitrariness of generalized functions in Schwartz distribution, linking it to infinities in quantum field theory, and explores methods to resolve this issue.

Contribution

It analyzes existing methods like Guttinger Konig and Hormander to address the product arbitrariness in generalized functions within quantum field theory.

Findings

Identifies the role of product arbitrariness in infinities in quantum field theory

Evaluates methods for eliminating arbitrariness in generalized functions

Provides insights into mathematical foundations of quantum corrections

Abstract

In this study, the problem of the product arbitrariness of generalised functions in the framework of Schwartz distribution is addressed. This arbitrariness is responsible for the problem of infinities encountered in quantum field theory when higher order corrections are considered. The methods of Guttinger Konig and Hormander for getting rid of this arbitrariness are investigated.