Fractional Derivative Regularization in QFT

TL;DR

This paper introduces a novel regularization method for quantum field theories using fractional derivatives, specifically Riesz fractional derivatives, to regularize loop integrals in scalar phi^4-theory.

Contribution

It proposes a new regularization technique replacing integer derivatives with fractional derivatives, demonstrated on scalar massless fields in phi^4-theory.

Findings

Regularized loop integrals depend on fractional order alpha.

Method applied successfully to scalar massless fields.

Potential for broader application in QFT regularization.

Abstract

In this paper, we propose new regularization, where integer-order differential operators are replaced by fractional-order operators. Regularization for quantum field theories based on application of the Riesz fractional derivatives of non-integer orders is suggested. The regularized loop integrals depend on parameter that is the order alpha>0 of the fractional derivative. The regularization procedure is demonstrated for scalar massless fields in phi^4-theory on n-dimensional pseudo-Euclidean space-time.