Path-Integral Approach to Scale Anomaly at Finite Temperature

Abstract

We derive the relativistic thermodynamic scale equation using imaginary-time path integrals, with complex scalar field theory taken as a concrete example. We use Fujikawa's method to derive the scaling anomaly for this system using a matrix regulator. We make a general scaling argument to show how for anomalous systems, the $\beta$ function of the vacuum theory can be derived from measurement of macroscopic thermodynamic parameters.

10 pages (this version is the published version)

References in corpus (6)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• QCD Thermodynamics from the Lattice
• Anomalous Commutator Algebra for Conformal Quantum Mechanics
• Path-Integral Derivation of the Non-relativistic Scale Anomaly
• Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions

Cited by in corpus (3)

• Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies
• Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly
• Dilational Symmetry-Breaking in Thermodynamics