Universal Definition of the Nonconformal Trace Anomaly

Area of Science:

• Theoretical Physics
• Quantum Field Theory

Background:

• Trace anomalies are crucial in quantum field theory, particularly for theories with conformal symmetry.
• Existing definitions of trace anomalies often assume classical conformal invariance, limiting their applicability.
• Previous proposals for generalized trace anomalies have faced controversies regarding their definition and use of classical equations of motion.

Purpose of the Study:

• To establish a generalized, universal definition for the trace anomaly in theories that are not conformally invariant at the classical level.
• To provide a definition compatible with any regularization scheme.
• To resolve existing controversies by clearly defining the extent to which classical equations of motion should be employed.

Main Methods:

• Development of a generalized definition for the trace anomaly.
• Demonstration of the definition's suitability for any regularization scheme.
• Analysis of the connection between the proposed trace anomaly definition and the functional Jacobian from a Weyl transformation.

Main Results:

• A generalized and universal notion of the trace anomaly has been established for theories without classical conformal invariance.
• The proposed definition is independent of the chosen regularization scheme.
• A clear link has been shown between this generalized trace anomaly and the functional Jacobian resulting from a Weyl transformation.

Conclusions:

• The established definition provides a robust framework for studying trace anomalies in a broader class of theories.
• This work resolves ambiguities and controversies in previous approaches to generalized trace anomalies.
• The findings offer new insights into the relationship between anomalies, Weyl transformations, and classical equations of motion in quantum field theory.