The Schrödinger-Virasoro Algebra

Mathematical structure and dynamical Schrödinger symmetries

  • Jérémie Unterberger
  • Claude Roger

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xlii
  2. Jérémie Unterberger, Claude Roger
    Pages 1-15
  3. Jérémie Unterberger, Claude Roger
    Pages 17-29
  4. Jérémie Unterberger, Claude Roger
    Pages 31-42
  5. Jérémie Unterberger, Claude Roger
    Pages 43-55
  6. Jérémie Unterberger, Claude Roger
    Pages 57-73
  7. Jérémie Unterberger, Claude Roger
    Pages 75-123
  8. Jérémie Unterberger, Claude Roger
    Pages 125-145
  9. Jérémie Unterberger, Claude Roger
    Pages 147-159
  10. Jérémie Unterberger, Claude Roger
    Pages 161-205
  11. Jérémie Unterberger, Claude Roger
    Pages 207-230
  12. Jérémie Unterberger, Claude Roger
    Pages 231-272
  13. Back Matter
    Pages 273-302

About this book

Introduction

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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Keywords

Conformal field theory Dirac-Lévy-Leblond equation and operator Ermakov-Lewis invariants Infinite-dimensional Lie algebras Schrödinger invariance, symmetry and Schrödinger-Virasoro algebra Space-time symmetries in physics Spectral Theory of Schrödinger operators supersymmetry

Authors and affiliations

  • Jérémie Unterberger
    • 1
  • Claude Roger
    • 2
  1. 1.Institut Elie CartanUniversité Henri PoincaréVandoeuvre-les-NancyFrance
  2. 2.Faculté des Sciences et Technologies, Departement MathematiquesUniversité Lyon IVilleurbanne CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22717-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-22716-5
  • Online ISBN 978-3-642-22717-2
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site
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