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 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 modelsof 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. First monographical account on newly discovered structures in mathematicalphysics. Provides an up-to-date and self-contained presentation. Connects various fields of applications in mathematical physics research. INDICE: Introduction. Geometric Definitions of SV. Basic Algebraic and Geometric Features. Coadjoint Representaion. Induced Representations and Verma Modules. Coinduced Representations. Vertex Representations. Cohomology, Extensions and Deformations. Action of sv on Schrödinger and Dirac Operators. Monodromy of Schrödinger Operators. Poisson Structures and Schrödinger Operators. Supersymmetric Extensions of sv. Appendix to chapter 6. Appendix to chapter 11. Index.

• ISBN: 978-3-642-22716-5
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 302
• Fecha Publicación: 31/10/2011
• Nº Volúmenes: 1
• Idioma: Inglés