### 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 language | English (US) |
---|---|

Pages (from-to) | 265-274 |

Number of pages | 10 |

Journal | Letters in Mathematical Physics |

Volume | 51 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2000 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 51, no. 4, pp. 265-274. https://doi.org/10.1023/A:1007692910159

}

TY - JOUR

T1 - Projectively equivariant quantization map

AU - Bouarroudj, Sofiane

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

KW - Modules of differential operators

KW - Projective connection

KW - Projective structures

KW - Quantization

UR - http://www.scopus.com/inward/record.url?scp=0001207593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001207593&partnerID=8YFLogxK

U2 - 10.1023/A:1007692910159

DO - 10.1023/A:1007692910159

M3 - Article

AN - SCOPUS:0001207593

VL - 51

SP - 265

EP - 274

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 4

ER -