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

• Main Authors: Unterberger, Jérémie (Author), Roger, Claude (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Theoretical and Mathematical Physics,
• Subjects: Physics.; Category theory (Mathematics).; Homological algebra.; Topological groups.; Lie groups.; Mathematical physics.; Statistical physics.; Dynamical systems.; Mathematical Methods in Physics.; Topological Groups, Lie Groups.; Mathematical Physics.; Category Theory, Homological Algebra.; Statistical Physics, Dynamical Systems and Complexity.

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-d...

Table of Contents:

• Introduction
• Geometric Definitions of SV
• Basic Algebraic and Geometric Features
• Coadjoint Representaion
• Induced Representations and Verma Modules
• Coinduced Representations
• Vertex Representations
• Cohomology, Extensions and Deformations
• Action of sv on Schrödinger and Dirac Operators
• Monodromy of Schrödinger Operators
• Poisson Structures and Schrödinger Operators
• Supersymmetric Extensions of sv
• Appendix to chapter 6
• Appendix to chapter 11
• Index.