An application of neutrix calculus to quantum field theory

TL;DR

This paper introduces neutrix calculus as a novel mathematical framework to handle divergent integrals in quantum field theory, leading to finite results and potentially simplifying complex theories like quantum gravity.

Contribution

It applies neutrix calculus to quantum field theory, providing a new method for finite renormalizations and accommodating effective field theories and quantum gravity.

Findings

Recovered standard physical results in renormalizable theories

Achieved finite renormalizations using neutrix calculus

Suggested improved manageability of quantum gravity theories

Abstract

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories appear to be more manageable.