Natural and projectively equivariant quantizations by means of Cartan connections

DOI10.1007/s11005-005-6783-4zbMath1091.53006arXivmath/0606554OpenAlexW2011417400MaRDI QIDQ2571660

Pierre Mathonet, Fabian Radoux

Publication date: 14 November 2005

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606554

zbMATH Keywords

Cartan connectionsdifferential operatorsquantization mapsprojective equivariant quantization

Mathematics Subject Classification ID

Geometric quantization (53D50) Linear and affine connections (53B05) (G)-structures (53C10) Projective connections (53B10)

Related Items (12)

Existence of natural and projectively equivariant quantizations ⋮ Modules of bilinear differential operators over the orthosymplectic superalgebra \(\mathfrak{osp}(1|2)\) ⋮ Explicit formula for the natural and projectively equivariant quantization ⋮ The space of \(m\)-ary differential operators as a module over the Lie algebra of vector fields ⋮ Projectively equivariant quantizations over the superspace \({\mathbb{R}^{p|q}}\) ⋮ On \(\mathfrak{osp}(p+1,q+1|2r)\)-equivariant quantizations ⋮ Existence of Natural and Conformally Invariant Quantizations of Arbitrary Symbols ⋮ Non-uniqueness of the natural and projectively equivariant quantization ⋮ A first approximation for quantization of singular spaces ⋮ Equivariant quantization of orbifolds ⋮ Decomposition of symmetric tensor fields in the presence of a flat contact pro jective structure ⋮ Geometric realizations of generalized algebraic curvature operators

Cites Work

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• Projectively equivariant quantization for differential operators acting on forms
• Examples of Thomas-Whitehead projective connections
• Equivariant symbol calculus for differential operators acting on forms
• The representation of projective spaces
• Projectively equivariant quantization map.
• Relating Thomas-Whitehead projective connections by a gauge transformation
• The projective connections of T. Y. Thomas and J. H. C. Whitehead applied to invariant connections
• Projectively equivariant symbol calculus
• IFFT-equivariant quantizations
• Nonlocality of equivariant star products on \(T^*(\mathbb{R}\mathbb{P}^n)\)
• Projectively equivariant quantization and symbol calculus: noncommutative hypergeometric functions.

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