The Schrdinger-Virasoro Algebra: Mathematical structure and dynamical Schrding [Hardcover]

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schr?dinger-Virasoro algebra. Just as Poincar? invariance or conformal (Virasoro) invariance play a key r?le 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.

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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 Schr?dinger operators.

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 Schr?dinger and Dirac Operators.- Monodromy of Schr?dinger Operators.- Poisson Structures and Schr?dinger Operators.- Supersymmetric Extensions of sv.- Appendix to chapter 6.- Appendix to chapter 11.- Index.

From the reviews:

This monograph presents an accurate and self-contained description of the so-called Schr?dinger-Virasoro algebra & . this book constitutes an excellent report on the actual status of research concerning the Schr?dinger-Virasoro group and its applications in physics. Many of the results presented are actually recent research results, and the conclusions open new and interesting possibilities for further applications. This monograph will certainly become one of the clã1