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  • © 2012

The Schrödinger-Virasoro Algebra

Mathematical structure and dynamical Schrödinger symmetries

  • First monographical account on newly discovered structures in mathematical physics
  • Provides an up-to-date and self-contained presentation
  • Connects various fields of applications in mathematical physics research
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xlii
  2. Geometric Definitions of \(\mathfrak{s}\mathfrak{v}\)

    • Jérémie Unterberger, Claude Roger
    Pages 1-15
  3. Basic Algebraic and Geometric Features

    • Jérémie Unterberger, Claude Roger
    Pages 17-29
  4. Coadjoint Representation of the Schrödinger–Virasoro Group

    • Jérémie Unterberger, Claude Roger
    Pages 31-42
  5. Induced Representations and Verma Modules

    • Jérémie Unterberger, Claude Roger
    Pages 43-55
  6. Coinduced Representations

    • Jérémie Unterberger, Claude Roger
    Pages 57-73
  7. Vertex Representations

    • Jérémie Unterberger, Claude Roger
    Pages 75-123
  8. Cohomology, Extensions and Deformations

    • Jérémie Unterberger, Claude Roger
    Pages 125-145
  9. Action of \(\mathfrak{s}\mathfrak{v}\) on Schrödinger and Dirac Operators

    • Jérémie Unterberger, Claude Roger
    Pages 147-159
  10. Monodromy of Schrödinger Operators

    • Jérémie Unterberger, Claude Roger
    Pages 161-205
  11. Poisson Structures and Schrödinger Operators

    • Jérémie Unterberger, Claude Roger
    Pages 207-230
  12. Supersymmetric Extensions of the Schrödinger–Virasoro Algebra

    • Jérémie Unterberger, Claude Roger
    Pages 231-272
  13. Back Matter

    Pages 273-302

About this book

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.

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)

Authors and Affiliations

  • Institut Elie Cartan, Université Henri Poincaré, Vandoeuvre-les-Nancy, France

    Jérémie Unterberger

  • Faculté des Sciences et Technologies, Departement Mathematiques, Université Lyon I, Villeurbanne Cedex, France

    Claude Roger

Bibliographic Information

Buy it now

Buying options

Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access