The fate of the trace anomaly in a finite formulation of field theory

TL;DR

This paper demonstrates that using the Taylor-Lagrange regularization scheme in finite 4D field theory eliminates the trace anomaly and preserves the canonical dimensions of quantum fields, avoiding typical quantum anomalies.

Contribution

It shows that the Taylor-Lagrange regularization scheme removes the trace anomaly and maintains canonical field dimensions without introducing extra scales.

Findings

No anomalous contribution to the trace of the energy-momentum tensor.

Quantum corrections do not induce trace anomalies in this scheme.

Canonical dimensions of quantum fields are preserved.

Abstract

Within the framework of the recently proposed Taylor-Lagrange regularization scheme - which leads to finite elementary amplitudes in $4$-dimensional space-time with no additional dimensionful scales - we show that the trace of the energy-momentum tensor does not show any anomalous contribution even though quantum corrections are considered. Moreover, since the only renormalization we can think of within this scheme is a finite renormalization of the bare parameters to give the physical ones, the canonical dimension of quantum fields is also preserved by the use of this regularization scheme.