Projectively equivariant quantization map

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

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