On anomalies in classical dynamical systems

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.

arXiv version is already official

References in corpus (5)

• Classical anomalies for spinning particles
• Poincare Invariance of a Quantized Duality Symmetric Theory
• An Example of Poincare Symmetry with a Central Charge
• How to superize Liouville equation
• Two-dimensional N=1,2 Supersymmetric Chiral and Dual Models

Cited by in corpus (7)

• Four types of (super)conformal mechanics: D-module reps and invariant actions
• On the Supersymmetrization of Galileon Theories in Four Dimensions
• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• How to superize Liouville equation
• Trace and diffeomorphism anomalies of the classical Liouville theory, Virasoro algebras, Weyl-gauging and all that
• Noncentral extensions as anomalies in classical dynamical systems