The Explicit Derivation of QED Trace Anomaly in Symmetry-Preserving Loop Regularization at One Loop Level

TL;DR

This paper explicitly derives the QED trace anomaly at one-loop level using a symmetry-preserving loop regularization method in 4D, demonstrating its consistency and comparing it with traditional regularization techniques.

Contribution

It provides a clear derivation of the QED trace anomaly using a novel regularization method that preserves gauge and Poincare symmetries at one loop.

Findings

Loop regularization reproduces the standard trace anomaly form.

The method is consistent and applicable to chiral and trace anomalies.

Comparison shows differences with Pauli-Villars and dimensional regularization.

Abstract

The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales, namely the ultraviolet (UV) cut-off $M_c$ and infrared (IR) cut-off $\mu_s$. It is shown that the dilation Ward identity which relates the three-point diagrams with the vacuum polarization diagrams gets the standard form of trace anomaly through quantum corrections in taking the consistent limit $M_c\to \infty$ and $\mu_s = 0$ which recovers the original integrals. This explicitly demonstrates that the loop regularization method is indeed a self-consistent regularization scheme which is applicable to the calculations not only for the chiral anomaly but also for the trace anomaly, at least at one-loop level. It is also seen that the consistency conditions which relates the tensor-type and scalar-type irreducible loop integrals (ILIs) are crucial for obtaining a consistent result. As a comparison, we also present the one-loop calculations by using the usual Pauli-Villars regularization and the dimensional regularization.