Determinants, Pfaffians and Quasi-Free Representations of the CAR Algebra

DOI10.1142/S0129055X98000227zbMath0917.46061MaRDI QIDQ4222547

Tilmann Wurzbacher, Mauro Spera

Publication date: 19 July 1999

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

zbMATH Keywords

isotropic Grassmanniandeterminant line bundlequasi-free statesHilbert space GrassmannianCAR algebrasBogolubov automorphismsBorel-Weil type descriptionPfaffian line bundlesSiegel manifold

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Coherent states (81R30) Classical real and complex (co)homology in algebraic geometry (14F25) Applications of functional analysis in quantum physics (46N50) Geometric quantization (53D50) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (8)

Twistor spaces and spinors over loop spaces ⋮ Unnamed Item ⋮ SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES ⋮ Isometric embeddings of infinite-dimensional Grassmannians ⋮ Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian ⋮ On Some Geometric Aspects of Coherent States ⋮ Banach algebras associated to Lax pairs ⋮ The Dirac-Ramond operator on loops in flat space

Cites Work

• Homogeneous vector bundles
• Loop groups and equations of KdV type
• Lorentz manifolds modelled on a Lorentz symmetric space
• The Pfaffian line bundle
• Representations of anticommutation relations and Bogolioubov transformations
• Free states of the canonical anticommutation relations
• On quasifree states of CAR and Bogoliubov automorphisms
• Pfaffians on Hilbert space
• Isometric imbedding of complex manifolds
• REMARKS ON CALABI'S DIASTASIS FUNCTION AND COHERENT STATES
• Spinors in n Dimensions

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