Deformation theory applied to quantization and statistical mechanics

DOI10.1007/BF00400978zbMath0567.58011OpenAlexW2086455759MaRDI QIDQ1059911

Henri Basart, Moshé Flato, André Lichnerowicz, Daniel Sternheimer

Publication date: 1984

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00400978

zbMATH Keywords

deformationquantizationsymplectic structureKMS-statesquantum statistical mechanics

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Quantum equilibrium statistical mechanics (general) (82B10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Foundations of thermodynamics and heat transfer (80A05) Geometric quantization (53D50)

Related Items

Cohomology and deformations of Lie superalgebras, Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow, Traces for Star Products on the Dual of a Lie Algebra, Quantum groups and deformation quantization: Explicit approaches and implicit aspects, The modular automorphism group of a Poisson manifold, Note on the super-extended Moyal formalism and its BBGKY hierarchy, Poisson geometry, On the regular Hilbert space representation of a Moyal quantization, DLR-KMS correspondence on lattice spin systems, Star product and invariant integration for Lie type noncommutative spacetimes, Quantization: Deformation and/or functor?, STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION, Remarks on the GNS Representation and the Geometry of Quantum States, Schwinger-Keldysh formalism. II: Thermal equivariant cohomology, An evolutionary view of quantum foundations, On the inverse mapping of the formal symplectic groupoid of a deformation quantization, Deformation quantization of a certain type of open systems, *-products on some Kähler manifolds, On the asymptotic behavior of the Wigner transform for large values of Planck's constant

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Regular * representations of Lie algebras
• Some ideas about quantization
• Déformation du crochet de Poisson sur une variété symplectique
• Deformation theory and quantization. I: Deformations of symplectic structures
• On the deformation of rings and algebras
• On the principles of elementary quantum mechanics