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

Couverture
Springer Science & Business Media, 25 oct. 2011 - 302 pages

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.

 

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Table des matières

Geometric Definitions of sv
1
Basic Algebraic and Geometric Features
17
Coadjoint Representation of the SchrödingerVirasoro Group
30
Induced Representations and Verma Modules
43
Coinduced Representations
57
Vertex Representations
74
Cohomology Extensions and Deformations
125
Action of sv on Schrödinger and Dirac Operators
146
Monodromy of Schrödinger Operators
161
Poisson Structures and Schrödinger Operators
206
Supersymmetric Extensions of the SchrödingerVirasoroAlgebra
231
Appendix to Chapter 6
273
Appendix to Chapter 11
281
References
292
Index
299
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