The geometry of real reducible polarizations in quantum mechanics

DOI10.1088/1751-8121/aa58c7zbMath1361.81083arXiv1608.00031OpenAlexW3100989038WikidataQ57555668 ScholiaQ57555668MaRDI QIDQ2975041

Carlos Prieto, Raffaele Vitolo

Publication date: 11 April 2017

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

Full work available at URL: https://arxiv.org/abs/1608.00031

zbMATH Keywords

geometric quantizationreal polarizationSchrödinger equation in curved spaces

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Geometry and quantization, symplectic methods (81S10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

• Fractional Fourier transform and geometric quantization
• Quantum Hall effect and Quillen metric
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• \(d_ f\)-cohomology of Lagrangian foliations
• Geometric quantization and quantum mechanics
• Geometric quantization and multiplicities of group representations
• Quantum mechanics of a spin particle in a curved spacetime with absolute time
• Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type
• Separable quantizations of Stäckel systems
• Fourier-Mukai transform and adiabatic curvature of spectral bundles for Landau Hamiltonians on Riemann surfaces
• Holomorphic spectral geometry of magnetic Schrödinger operators on Riemann surfaces
• On the BKS pairing for Kähler quantizations of the cotangent bundle of a Lie group
• On the geometry of the energy operator in quantum mechanics
• Geometric Aspects of the Quantization of a Rigid Body
• Gauge Invariant Quantization on Riemannian Manifolds
• Quantization of a particle in a background Yang–Mills field
• Supersymmetry and the Atiyah–Singer index theorem. II. The scalar curvature factor in the Schrödinger equation
• Covariant Schr dinger operator
• Quantization in singular real polarizations: Kähler regularization, Maslov correction and pairings
• A covariant approach to the quantization of a rigid body
• Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles
• Riemannian geometry
• Quantization and spectral geometry of a rigid body in a magnetic monopole field
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