Projective flatness in the quantisation of bosons and fermions

DOI10.1063/1.4923409zbMath1330.81136arXiv1008.5333OpenAlexW1621383338MaRDI QIDQ5500742

Siye Wu

Publication date: 10 August 2015

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

Full work available at URL: https://arxiv.org/abs/1008.5333

zbMATH Keywords

geodesicscut locuscomplex structureparallel transportflat connectiongeometric quantizationlinear fermionic system, bosonic system

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) Geometry and quantization, symplectic methods (81S10) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Geometric quantization (53D50) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

Related Items

Representations of fermionic star product algebras and the projectively flat connection, Quantisation of a family of phase spaces

Cites Work

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• Geometric quantization, parallel transport and the Fourier transform
• Geometric quantization of Chern-Simons gauge theory
• Stratified symplectic spaces and reduction
• Algèbre de Clifford symplectique, revetements du groupe symplectique, indices de Maslov et spineurs symplectiques
• On cut loci of compact symmetric spaces
• Quantization of algebraic cones and Vogan's conjecture
• Die Eindeutigkeit der Schrödingerschen Operatoren
• Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type
• Holomorphic slices, symplectic reduction and multiplicities of representations
• Unitarity in ``Quantization commutes with reduction
• On the BKS pairing for Kähler quantizations of the cotangent bundle of a Lie group
• The cut locus and conjugate locus of a riemannian manifold
• Quantization of Chern-Simons gauge theory with complex gauge group
• Flat connections and geometric quantization
• Minimum and Conjugate Points in Symmetric Spaces
• Coherent states and projective representation of the linear canonical transformations
• Geometric quantization and the Bogoliubov transformation
• Marsden–Weinstein reduction on graded symplectic manifolds
• Geometric Quantization and No Go Theorems
• Conjugate loci in Grassmann manifolds
• Invariant Affine Connections on Homogeneous Spaces
• On the Theory of Automorphic Functions of a Matrix Variable I-Geometrical Basis
• Symplectic Geometry