The Schrödinger-Virasoro Algebra

Mathematical structure and dynamical Schrödinger symmetries

Nonfiction, Science & Nature, Mathematics, Group Theory, Science, Physics, Mathematical Physics
Cover of the book The Schrödinger-Virasoro Algebra by Jérémie Unterberger, Claude Roger, Springer Berlin Heidelberg
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Author: Jérémie Unterberger, Claude Roger ISBN: 9783642227172
Publisher: Springer Berlin Heidelberg Publication: October 25, 2011
Imprint: Springer Language: English
Author: Jérémie Unterberger, Claude Roger
ISBN: 9783642227172
Publisher: Springer Berlin Heidelberg
Publication: October 25, 2011
Imprint: Springer
Language: English

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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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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