1978
DOI: 10.1016/0003-4916(78)90224-5
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Deformation theory and quantization. I. Deformations of symplectic structures

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Cited by 1,351 publications
(893 citation statements)
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“…There is no a priori reference to states, or any probabilistic interpretation, so the quantum theory presents a smooth deviation away from the classical Liouville equation [93,94,95,96].…”
Section: Phase-space Approachmentioning
confidence: 99%
“…There is no a priori reference to states, or any probabilistic interpretation, so the quantum theory presents a smooth deviation away from the classical Liouville equation [93,94,95,96].…”
Section: Phase-space Approachmentioning
confidence: 99%
“…A possible alternative to quantize Nambu bracket by deformation quantization [2], [3] was discussed in [20] (see Sect. 2.2 for a brief review on star-products).…”
Section: Difficulties With Usual Quantizationsmentioning
confidence: 99%
“…For completeness we give here a brief review on deformation quantization and star-products; a full treatment can be found in [2], [3] and a recent review in [10]. Let M be a Poisson manifold.…”
Section: Deformation Quantizationmentioning
confidence: 99%
“…where {·, ·} is the Poisson bracket defined by w. For some earlier results on star products on symplectic manifolds, see Bayen et al [1], De Wilde-Lecomte [5], Fedosov [6]. In general a Z-graded commutative algebra may have a deformation by Z 2 -graded commutative algebras, e.g.…”
Section: Huai-dong Cao and Jian Zhou (Communicated By Richard Schoen)mentioning
confidence: 99%
“…Notice that it now suffices to find the eigenvalues of M h on Λ [0] h,h −1 (V * ) and Λ [1] h,h −1 (V * ). In Cao-Zhou [4], this is done by induction on the dimension of V .…”
Section: Furthermore If We Regard Multiplications By H and H −1 As Omentioning
confidence: 99%