Dimensional Regularization in Quantum Field Theory with Ultraviolet Cutoff

TL;DR

This paper introduces a new regularization scheme called detached regularization that extends dimensional regularization to quantum field theories with an ultraviolet cutoff, allowing independent treatment of divergences.

Contribution

The work develops and demonstrates a novel regularization method that preserves properties of dimensional regularization while accommodating an ultraviolet cutoff in QFTs.

Findings

Detached regularization separates power-law and logarithmic divergences.

Application to vacuum energy and QED shows effective divergence handling.

Case study confirms two-loop effectiveness in scalar self-energy.

Abstract

In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way preserving all the properties of the dimensional regularization. And we find that it can indeed be. The resulting extension gives a framework in which the power-law and logarithmic divergences get detached to involve different scales. This new regularization scheme, the detached regularization as we call it, enables one to treat the power-law and logarithmic divergences differently and independently. We apply the detached regularization to the computation of the vacuum energy and to two well-known QFTs namely the scalar and spinor electrodynamics. As a case study, we consider Fujikawa's subtractive renormalization in the framework of the detached regularization, and show its effectiveness up to two loops by specializing to scalar self energy. We discuss various application areas of the detached regularization.