A note on quantum Hamiltonian reduction and anomalies

B. M. Elfimov, A. A. Sharapov

Tomsk State University, Tomsk, Russia

Abstract: When quantizing field-theoretical models with gauge symmetries, quantum anomalies are often encountered. It is commonly believed that the cause of these anomalies lies in the infinite numbers of degrees of freedom, which requires the field system to be completed within a suitable regularization and renormalization scheme. We present an example of a finite-dimensional Hamiltonian system with first-class constraints, whose quantization leads to unavoidable quantum anomalies. These anomalies arise due to the nontrivial topology of the reduced phase space of the system.

Keywords: BRST theory, first-class constraints, Hamiltonian reduction, deformation quantization, quantum anomalies.

PACS: 11.10.Ef

MSC: 81S10

Received: 03.03.2025
Revised: 15.06.2025

DOI: 10.4213/tmf10974

 English version: Theoretical and Mathematical Physics, 2025, 225:2, 2007–2016

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