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

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

by Jérémie Unterberger, Claude Roger


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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.

Product Details

ISBN-13: 9783642269592
Publisher: Springer Berlin Heidelberg
Publication date: 11/28/2013
Series: Theoretical and Mathematical Physics
Edition description: 2012
Pages: 302
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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.

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