Mathematical structure and dynamical Schrödinger symmetries
Unterberger, Jérémie, Roger, Claude
2012, XLII, 302 p.
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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 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.
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Content Level » Research
Keywords » Conformal field theory - Dirac-Lévy-Leblond equation and operator - Ermakov-Lewis invariants - Infinite-dimensional Lie algebras - Schrödinger invariance, symmetry and - Schrödinger-Virasoro algebra - Space-time symmetries in physics - Spectral Theory of Schrödinger operators - supersymmetry
Related subjects » Algebra - Complexity - Theoretical, Mathematical & Computational Physics
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