On anomalies in classical dynamical systems

TL;DR

This paper introduces the concept of classical anomalies in dynamical systems, where symmetries lead to centrally extended algebras of conserved charges, with explicit examples and potential applications discussed.

Contribution

It defines classical anomalies, derives conditions for their occurrence, and provides explicit two-dimensional model examples illustrating the phenomenon.

Findings

Classical anomalies involve centrally extended symmetry algebras.

Explicit two-dimensional models demonstrate the existence of classical anomalies.

The paper suggests further research directions and applications.

Abstract

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure, close an algebra which is just the centrally extended version of the original symmetry algebra. The consistency conditions for this to occur are derived. Explicit examples are given based on simple two-dimensional models. Applications of the above scheme and lines of further investigations are suggested.