Dimensional regularization in quantum field theory with ultraviolet cutoff

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 that preserves all the properties of the dimensional regularization. And we find that it can indeed be achieved. 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 quantum field theories, 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.

Automated summary

In this study, we investigate whether the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff while preserving all its properties. We find that this extension is indeed possible. The resulting detached regularization separates power-law and logarithmic divergences at different scales, allowing for independent treatment of these divergences. We apply the detached regularization to calculate vacuum energy and analyze two well-known quantum field theories. We also explore the effectiveness of the detached regularization in the subtractive renormalization method and discuss its potential applications.