Index and dynamics of quantized contact transformations

Steven Zelditch

Displaying similar documents to “Index and dynamics of quantized contact transformations”

Semiclassical spectral estimates for Toeplitz operators

David Borthwick, Thierry Paul, Alejandro Uribe (1998)

Annales de l'institut Fourier

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Let $X$ be a compact Kähler manifold with integral Kähler class and $L \to X$ a holomorphic Hermitian line bundle whose curvature is the symplectic form of $X$ . Let $H \in C^{\infty} (X, ℝ)$ be a Hamiltonian, and let $T_{k}$ be the Toeplitz operator with multiplier $H$ acting on the space $ℋ_{k} = H^{0} (X, L^{\otimes k})$ . We obtain estimates on the eigenvalues and eigensections of $T_{k}$ as $k \to \infty$ , in terms of the classical Hamilton flow of $H$ . We study in some detail the case when $X$ is an integral coadjoint orbit of a Lie group.

Quantum ergodicity of C*-dynamical systems

Steven Zelditch (1994-1995)

Séminaire de théorie spectrale et géométrie

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Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

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We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians....

Toeplitz Quantization for Non-commutating Symbol Spaces such as $S U_{q} (2)$

Stephen Bruce Sontz (2016)

Communications in Mathematics

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Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $S U_{q} (2)$ is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples...

Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results.

Schlichenmaier, Martin (2010)

Advances in Mathematical Physics

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On the index theorem for symplectic orbifolds

Boris Fedosov, Bert-Wolfang Schulze, Nikolai Tarkhanov (2004)

Annales de l’institut Fourier

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We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.

Mathematical foundations of geometric quantization.

Arturo Echeverría-Enriquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy, Carles Victoria-Monge (1998)

Extracta Mathematicae

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Toeplitz operators, Kähler manifolds, and line bundles.

Foth, Tatyana (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Fourier-like kernels in geometric quantization

K. Gawędzki

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CONTENTSI. Introduction............................................................................................................................................... 5II. Preliminary notions................................................................................................................................ 7III. Geometric quantization.........................................................................................................................12 A. Elements of...