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The QED trace anomaly is calculated at one-loop level based on the loopregularization method which is realized in 4-dimensional spacetime andpreserves gauge symmetry and Poincare symmetry in spite of the introduction oftwo 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 thethree-point diagrams with the vacuum polarization diagrams gets the standardform of trace anomaly through quantum corrections in taking the consistentlimit $M_c\to \infty$ and $\mu_s = 0$ which recovers the original integrals.This explicitly demonstrates that the loop regularization method is indeed aself-consistent regularization scheme which is applicable to the calculationsnot only for the chiral anomaly but also for the trace anomaly, at least atone-loop level. It is also seen that the consistency conditions which relatesthe tensor-type and scalar-type irreducible loop integrals (ILIs) are crucialfor obtaining a consistent result. As a comparison, we also present theone-loop calculations by using the usual Pauli-Villars regularization and thedimensional regularization.

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