The Schrödinger-Virasoro Algebra [electronic resource] : Mathematical structure and dynamical Schrödinger symmetries /
Unterberger, Jérémie.author.
Roger, Claude.author.
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. .
Description based upon print version of record.
Includes bibliographical references and index.
Introduction -- Geometric Definitions of SV -- Basic Algebraic and Geometric Features -- Coadjoint Representation -- 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.
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. .
Physics.
Topological groups.
Lie groups.
Mathematical physics.
Category theory (Mathematics).
Homological algebra.
Statistical physics.
Dynamical systems.
Mathematical Methods in Physics.
Topological Groups, Lie Groups.
Mathematical Physics.
Category Theory, Homological Algebra.
Complex Systems.
Statistical Physics and Dynamical Systems.

Theoretical and Mathematical Physics