An Explicit Formula for the Natural and Conformally Invariant Quantization

被引：0
作者：
Fabian Radoux
机构：
[1] University of Liège,Institute of Mathematics
来源：
Letters in Mathematical Physics | 2009年 / 89卷
关键词：
53B05; 53A30; 53D50; 53C10; conformal Cartan connections; differential operators; natural maps; quantization maps;
D O I：
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学科分类号：
摘要：
Lecomte (Prog Theor Phys Suppl 144:125–132, 2001) conjectured the existence of a natural and conformally invariant quantization. In Mathonet and Radoux (Existence of natural and conformally invariant quantizations of arbitrary symbols, math.DG 0811.3710), we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the method used in Mathonet and Radoux and to tools already used in Radoux [Lett Math Phys 78(2):173–188, 2006] in the projective setting. This formula is extremely similar to the one giving the natural and projectively invariant quantization in Radoux.
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页码：249 / 263
页数：14
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共 18 条
[1]  
Bouarroudj S.(2001)Formula for the projectively invariant quantization on degree three C. R. Acad. Sci. Paris Sér. I Math. 333 343-346
[2]  
Čap A.(1997)Invariant operators on manifolds with almost Hermitian symmetric structures. I. Invariant differentiation Acta Math. Univ. Comenian. (N.S.) 66 33-69
[3]  
Slovák J.(1999)Conformally equivariant quantization: existence and uniqueness Ann. Inst. Fourier (Grenoble) 49 1999-2029
[4]  
Souček V.(2001)Conformally equivariant quantum Hamiltonians Selecta Math. (N.S.) 7 291-320
[5]  
Duval C.(2001)Projectively equivariant quantization and symbol calculus: noncommutative hypergeometric functions Lett. Math. Phys. 57 61-67
[6]  
Lecomte P.(2005)Higher symmetries of the Laplacian Ann. Math. (2) 161 1645-1665
[7]  
Ovsienko V.(2001)Towards projectively equivariant quantization Prog. Theor. Phys. Suppl. 144 125-132
[8]  
Duval C.(1999)Projectively equivariant symbol calculus Lett. Math. Phys. 49 173-196
[9]  
Ovsienko V.(2007)Cartan connections and natural and projectively equivariant quantizations Lond. Math. Soc. 76 87-104
[10]  
Duval C.(2006)Explicit formula for the natural and projectively equivariant quantization Lett. Math. Phys. 78 173-188
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