Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles

DOI10.1142/S0129055X16500197zbMath1351.81064OpenAlexW2164513089MaRDI QIDQ2829629

Nicolaas P. Landsman

Publication date: 8 November 2016

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

Full work available at URL: https://doi.org/10.1142/s0129055x16500197

zbMATH Keywords

deformation quantizationidentical particles\(C^{\ast}\)-algebrasmultiply connected spaces

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) General theory of (C^*)-algebras (46L05) Applications of selfadjoint operator algebras to physics (46L60) Many-body theory; quantum Hall effect (81V70) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator algebra methods applied to problems in quantum theory (81R15) Equivariant homotopy theory in algebraic topology (55P91) Deformations of fiber bundles (32G08) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (6)

Two approaches to fractional statistics in the quantum Hall effect: idealizations and the curious case of the anyon ⋮ Idealizations, essential self-adjointness, and minimal model explanation in the Aharonov-Bohm effect ⋮ Philosophical issues concerning phase transitions and anyons: emergence, reduction, and explanatory fictions ⋮ Infinitesimal idealization, easy road nominalism, and fractional quantum statistics ⋮ A generalization of the one-dimensional boson-fermion duality through the path-integral formalism ⋮ Manifold topology, observables, and gauge group

Cites Work

• The role of symmetry in the interpretation of physical theories
• The Conventionality of Parastatistics
• Morita equivalence and characteristic classes of star products
• QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS
• QUANTIZATION AND SUPERSELECTION SECTORS II: DIRAC MONOPOLE AND AHARONOV-BOHM EFFECT
• Indistinguishable Classical Particles
• Principles of harmonic analysis
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