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Sunday, February 9, 2020 | History

4 edition of Quantization of singular symplectic quotients found in the catalog.

Quantization of singular symplectic quotients

Quantization of singular symplectic quotients

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  • 25 Currently reading

Published by Birkhäuser Verlag in Basel, Boston .
Written in English

    Subjects:
  • Symplectic manifolds,
  • Geometric quantization

  • Edition Notes

    Includes bibliographical references

    StatementN.P. Landsman, M. Pflaum, M. Schlichenmaier, editors
    SeriesProgress in mathematics -- v. 198, Progress in mathematics (Boston, Mass.) -- vol. 198
    ContributionsLandsman, N. P., Pflaum, M., Schlichenmaier, Martin, 1952-
    Classifications
    LC ClassificationsQA641 .Q83 2001
    The Physical Object
    Paginationxii, 355 p. ;
    Number of Pages355
    ID Numbers
    Open LibraryOL18128407M
    ISBN 103764366087, 0817666087
    LC Control Number2001043134

    The mapping torus of a contact diffeomorphism admits a folded symplectic structure. MathSci reviews of my published papers, including links to online versions of many of them may be found here. Lectures on the Geometry of Quantization, by S. Tian and W.

    However, as a natural quantization scheme a functorWeyl's map is not satisfactory. This quantization is a virtual representation of G, in which each irreducible representation appears with a finite multiplicity. Zhang, An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg, Inv. Index of contact diffeomorphisms and folded symplectic structures A folded symplectic structure is a closed 2-form which is nondegenerate except on a hypersurface, called the folding hypersurface, and whose restriction to that hypersurface has maximal rank. The modular automorphism group of a Poisson manifold appeared in Journal of Geometry and Physics Tangential deformation quantization and polarized symplectic groupoids appeared in Deformation Theory and Symplectic Geometry, S.

    In the case the variety has finitely many symplectic leaves such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groupsthe D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. Cattaneo, A. Geometric quantization[ edit ] The geometric quantization procedure falls into the following three steps: prequantization, polarization, and metaplectic correction. Lauter, R.


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Quantization of singular symplectic quotients book

We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein—Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions.

Teleman, The quantization conjecture revisited,math. Let L be a positive G-equivariant line bundle over X. Calculus Unlimited, by J. You may need to download the file remark. These classes of systems are as natural and fundamental as conservative mechanical systems.

Quantization of non-compact Hamiltoninan G-spaces In the first part of the talk I will present a new regularized version of an index of a Dirac operator on a complete Riemannian manifold endowed with an action of a compact Lie group G.

Lebeau, Complex immersions and Quillen metrics,Publ. Math 67— Velhinho, J. Brown, Ronald and Icen, I. Sjamaar, Singular reduction and quantization, Topology 38— Download preview PDF.

Prequantization produces a natural Hilbert space together with a quantization procedure for observables that exactly transforms Poisson brackets on the classical side into commutators on the quantum side. Skandalis, G. Sternheimer, eds. This is a preview of subscription content, log in to check access.

However, as a natural quantization scheme a functorWeyl's map is not satisfactory. Sternberg, Geometric quantization and multiplicities of group representations, Inv.

Link to online version. Index of contact diffeomorphisms and folded symplectic structures A folded symplectic structure is a closed 2-form which is nondegenerate except on a hypersurface, called the folding hypersurface, and whose restriction to that hypersurface has maximal rank.We then de ne the quantization of the singular quotient T G==AdGas the kernel of the (twisted) Dolbeault{Dirac operator on the principal stratum, and show that quantization commutes with reduction in the sense that either way one obtains the same Hilbert space L2(T)W(G;T).

List of publications by sylvaindez.com N.P. (Klaas) Landsman (August ) Quantization of Singular Symplectic Quotients (Birkh auser, Basel, ).

With M. P aum & M. Schlichenmaier. 2.

Singular unitarity in

The Challenge of Chance (Springer, Zug, ). With E. van Wolde. Book chapters 1. Quantized reduction as a tensor product. Quantization of Singular Symplectic Quo. Buy Quantization of Singular Symplectic Quotients (Progress in Mathematics) on sylvaindez.com FREE SHIPPING on qualified ordersAuthor: N.P.

Landsman. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Let M be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G. Let M//G = M0 be the symplectic quotient at value 0 of the moment map φ.

The space M0 is in general a complex analytic stratified Kähler space (see [4] for this notion). Quantization of Singular Symplectic Quotients.

Editors: Landsman, N.P., Pflaum, Markus, Schlichenmaier, Martin (Eds.) Free Preview. Buy this book eBook ,14 Services for this Book. Download Product Flyer Download High-Resolution Cover. Facebook Twitter LinkedIn Google++. Recommended for you. Abstract: Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion.

The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is equal to the Riemann-Roch number of the symplectic quotient of M, provided the quotient is sylvaindez.com: Eckhard Meinrenken, Reyer Sjamaar.