The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical Schrödinger symmetriesSpringer Science & Business Media, 25 oct. 2011 - 302 pages 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 rôle 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. |
Table des matières
Geometric Definitions of sv | 1 |
Basic Algebraic and Geometric Features | 17 |
Coadjoint Representation of the SchrödingerVirasoro Group | 30 |
Induced Representations and Verma Modules | 43 |
Coinduced Representations | 57 |
Vertex Representations | 74 |
Cohomology Extensions and Deformations | 125 |
Action of sv on Schrödinger and Dirac Operators | 146 |
Monodromy of Schrödinger Operators | 161 |
Poisson Structures and Schrödinger Operators | 206 |
Supersymmetric Extensions of the SchrödingerVirasoroAlgebra | 231 |
Appendix to Chapter 6 | 273 |
Appendix to Chapter 11 | 281 |
References | 292 |
Index | 299 |
Autres éditions - Tout afficher
The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical ... Jérémie Unterberger,Claude Roger Aucun aperçu disponible - 2011 |
The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical ... Jérémie Unterberger,Claude Roger Aucun aperçu disponible - 2013 |
The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical ... Jérémie Unterberger,Claude Roger Aucun aperçu disponible - 2011 |