arXiv subjects

Marcela Zuccalli

Publications and source records attributed to Marcela Zuccalli.

21 records · Page 2Linked to original sources

arXiv2010

Lagrangian reduction of nonholonomic discrete mechanical systems

In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the reduction process is a discrete dynamical system that we call the discrete reduced system. We illustrate the techniques by analyzing two types of discrete symmetric systems where it is possible to go further and obtain (forced) discrete mechanical systems that determine the dynamics of the discrete reduced system.

math.DG↗

arXiv2009

On Quantum Momentum Maps associated to non Ad*-equivariant Classical Momentum Maps

In an interesting work M.F. Muller-Bahns and N. Neumaier ("Some remarks on g-invariant Fedosov star products and quantum momentum mappings". Journal of Geometry and Physics 50 (2004), 257-272.) analyze the existence of a quantum momentum map based on the existence of a classical momentum map providing an answer to the proposal given by P. Xu in ("Fedosov *-products and quantum momentum maps". Commun. Math. Phys (1998) 167-197). In both papers only equivariant classical momentum maps are considered. In these notes, we extend Muller-Bahns and Neumaier analysis to the case of a non equivariant momentum map. In addition, we propose the notion of an anomalous quantum momentum map as an alternative to recover a non equivariant momentum map at the classical level by considering central extensions of the Lie algebra associated with non equivariance.

math-ph↗

arXiv2003

Noncentral extensions as anomalies in classical dynamical systems

A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001) 518-533] so as to encompass some extensions of Lie algebras related to noncanonical actions.

math.SG↗