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© 2012

The Schrödinger-Virasoro Algebra

Mathematical structure and dynamical Schrödinger symmetries

Book

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

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

Bibliographic information

Industry Sectors
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Reviews

From the reviews:

“This monograph presents an accurate and self-contained description of the so-called Schrödinger-Virasoro algebra … . this book constitutes an excellent report on the actual status of research concerning the Schrödinger-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 canonical references in the subject.” (Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1237, 2012)