Projectively equivariant quantization map

Sofiane Bouarroudj

    Research output: Contribution to journalArticle

    Abstract

    Let M be a manifold endowed with a symmetric affine connection Γ. The aim of this Letter is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T* M and the space of second-order linear differential operators, both viewed as modules over the group of diffeomorphisms and the Lie algebra of vector fields on M. This map is an isomorphism, for almost all values of certain constants, and it depends only on the projective class of the affine connection Γ.

    Original languageEnglish (US)
    Pages (from-to)265-274
    Number of pages10
    JournalLetters in Mathematical Physics
    Volume51
    Issue number4
    DOIs
    StatePublished - Jan 1 2000

    Fingerprint

    Affine Connection
    Equivariant
    Quantization
    Group of Diffeomorphisms
    isomorphism
    Cotangent Bundle
    Linear Differential Operator
    differential operators
    bundles
    Vector Field
    Isomorphism
    Lie Algebra
    polynomials
    algebra
    modules
    Module
    Polynomial
    Class

    Keywords

    • Modules of differential operators
    • Projective connection
    • Projective structures
    • Quantization

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Projectively equivariant quantization map. / Bouarroudj, Sofiane.

    In: Letters in Mathematical Physics, Vol. 51, No. 4, 01.01.2000, p. 265-274.

    Research output: Contribution to journalArticle

    Bouarroudj, Sofiane. / Projectively equivariant quantization map. In: Letters in Mathematical Physics. 2000 ; Vol. 51, No. 4. pp. 265-274.
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