The Schrödinger-Virasoro Algebra : Mathematical structure and dynamical Schrödinger symmetries. 1st ed. 2012

種類:

電子ブック

責任表示:

by Jérémie Unterberger, Claude Roger

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012

著者名:

• Unterberger, Jérémie.
• Roger, Claude.
• SpringerLink (Online service)

シリーズ名:

Theoretical and Mathematical Physics ;

ISBN:

9783642227172 [3642227171]    

注記:

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.
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. .

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