Cargando…

The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical Schrödinger symmetries

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-d...

Descripción completa

Detalles Bibliográficos
Autores principales: Unterberger, Jérémie, Roger, Claude
Lenguaje:eng
Publicado: Springer 2012
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-642-22717-2
http://cds.cern.ch/record/1399172
Descripción
Sumario:This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.   The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators. .