2004/10/31 by E. Gozzi, D. Mauro, A. Silvestri +1 · 1 citation
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Chiral anomaly #Classical mechanics #Computer science #Invariant (physics) #Mathematical physics #Mathematics #Measure (data warehouse) #Numerical methods for differential equations #Path integral formulation #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum field theory #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1142/s0217751x05025085
published as Int.J.Mod.Phys. A20 (2005) 5009-5036 · 26 pages, Latex, misprint fixed, a dedication included
arxiv created 2004/12/17 · openalex publication_date 2005/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the quantum path integral formulation of a field theory model an anomaly arises when the functional measure is not invariant under a symmetry transformation of the Lagrangian. In this paper, generalizing previous work done on the point particle, we show that even at the classical level we can give a path integral formulation for any field theory model. Since classical mechanics cannot be affected by anomalies, the measure of the classical path integral of a field theory must be invariant under the symmetry. The classical path integral measure contains the fields of the quantum one plus some extra auxiliary ones. So, at the classical level, there must be a sort of "cancellation" of the quantum anomaly between the original fields and the auxiliary ones. In this paper we prove in detail how this occurs for the chiral anomaly.