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Ouvrages Année : 2012

The Schrödinger-Virasoro algebra. Mathematical structure and dynamical Schrödinger symmetries.

Jeremie Unterberger
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Résumé

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 on 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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Dates et versions

hal-01321255 , version 1 (25-05-2016)

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  • HAL Id : hal-01321255 , version 1

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Jeremie Unterberger. The Schrödinger-Virasoro algebra. Mathematical structure and dynamical Schrödinger symmetries.. 2012, Theoretical and Mathematical Physics, 978-3-642-22716-5. ⟨hal-01321255⟩
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