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Joseph Dito 《Letters in Mathematical Physics》1990,20(2):125-134
The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the holomorphic representation and the star-exponential is established for the interacting scalar fields. 相似文献
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Giuseppe Dito 《Communications in Mathematical Physics》2015,338(2):523-532
In the context of formal deformation quantization, we provide an elementary argument showing that any universal quantization formula necessarily involves graphs with wheels. 相似文献
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Letters in Mathematical Physics - 相似文献
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We show that on the dual of a Lie algebra g of dimension d, the star product recently introduced by M. Kontsevich is equivalent to the Gutt star product on g*. We give an explicit expression for the operator realizing the equivalence between these star products. 相似文献
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Deformation quantization and Nambu Mechanics 总被引:3,自引:0,他引:3
G. Dito M. Flato D. Sternheimer L. Takhtajan 《Communications in Mathematical Physics》1997,183(1):1-22
Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After
considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization problem
is presented in the novel approach of Zariski quantization of fields (observables, functions, in this case polynomials). This
quantization is based on the factorization over ℝ of polynomials in several real variables. We quantize the infinite-dimensional
algebra of fields generated by the polynomials by defining a deformation of this algebra which is Abelian, associative and
distributive. This procedure is then adapted to derivatives (needed for the Nambu brackets), which ensures the validity of
the Fundamental Identity of Nambu Mechanics also at the quantum level. Our construction is in fact more general than the particular
case considered here: it can be utilized for quite general defining identities and for much more general star-products.
Supported by the European Commission and the Japan Society for the Promotion of Science.
NSF grant DMS-95-00557
This article was processed by the author using the LATEX style filepljour1 from Springer-Verlag. 相似文献
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Joseph Dito 《Letters in Mathematical Physics》1993,27(1):73-80
Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theø
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-theory by introducing a-dependent *-product cohomologically equivalent to the normal *-product. 相似文献
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An Algebra of Deformation Quantization for Star-Exponentials on Complex Symplectic Manifolds 总被引:1,自引:0,他引:1
The cotangent bundle T
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X to a complex manifold X is classically endowed with the sheaf of k-algebras of deformation quantization, where k := is a subfield of . Here, we construct a new sheaf of k-algebras which contains as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If P is any section of order zero of , we show that is well defined in . 相似文献
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