Theoretical and Mathematical Physics

The Schrödinger-Virasoro Algebra

Mathematical structure and dynamical Schrödinger symmetries

Authors: Unterberger, Jérémie, Roger, Claude

  • 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
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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)


Table of contents (11 chapters)

  • Geometric Definitions of $$\mathfrak{s}\mathfrak{v}$$

    Unterberger, Jérémie (et al.)

    Pages 1-15

  • Basic Algebraic and Geometric Features

    Unterberger, Jérémie (et al.)

    Pages 17-29

  • Coadjoint Representation of the Schrödinger–Virasoro Group

    Unterberger, Jérémie (et al.)

    Pages 31-42

  • Induced Representations and Verma Modules

    Unterberger, Jérémie (et al.)

    Pages 43-55

  • Coinduced Representations

    Unterberger, Jérémie (et al.)

    Pages 57-73

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-22717-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-642-22716-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-3-642-26959-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Schrödinger-Virasoro Algebra
Book Subtitle
Mathematical structure and dynamical Schrödinger symmetries
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22717-2
DOI
10.1007/978-3-642-22717-2
Hardcover ISBN
978-3-642-22716-5
Softcover ISBN
978-3-642-26959-2
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XLII, 302
Topics