Projectively equivariant quantization map

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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
Issue number4
StatePublished - Mar 2000


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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