Fractional Derivative Regularization in QFT

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.