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In mathematics, the Moyal product (after José Enrique Moyal; also called the star product or Weyl–Groenewold product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space star product. It is an associative, non-commutative product, ★, on the functions on ℝ2n, equipped with its Poisson bracket (with a generalization to symplectic manifolds, described below). It is a special case of the ★-product of the "algebra of symbols" of a universal enveloping algebra.

Attributes	Values
rdfs:label	Moyal-Produkt (de) Moyal product (en) Произведение Мояля (ru)
rdfs:comment	Das Moyal-Produkt (nach José Enrique Moyal), auch Weyl–Groenewold-Produkt (nach Hermann Weyl und ), ist in der Mathematik eine zweistellige Verknüpfung auf dem Funktionenraum der glatten Funktionen über . Das assoziative, nicht-kommutative Produkt ist ein Spezialfall des Sternproduktes auf allgemeinen Poisson-Mannigfaltigkeiten. Das Moyal-Produkt ist eine „Deformierungsquantisierung“ einer linearen Poisson-Mannigfaltigkeit, das heißt, die Algebra der klassischen Observablen wird deformiert, sodass eine nicht-kommutative Algebra von Quanten-Observablen entsteht (Quantisierung). (de) In mathematics, the Moyal product (after José Enrique Moyal; also called the star product or Weyl–Groenewold product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space star product. It is an associative, non-commutative product, ★, on the functions on ℝ2n, equipped with its Poisson bracket (with a generalization to symplectic manifolds, described below). It is a special case of the ★-product of the "algebra of symbols" of a universal enveloping algebra. (en) Произведением Мояля — самый известный пример звёздного произведения в фазовом пространстве. Оно является ассоциативным коммутативным звёздного произведением функций на ℝ2n, оснащённым скобкой Пуассона (с обобщением на симплектические многообразия, см. ниже). Это особый случай звёздного произведения «алгебры символов» в универсальной обертывающей алгебре. Названо в честь израильского учёного Хосе Энрике Мояля. (ru)
dcterms:subject	Mathematical physics Mathematical quantization
Wikipage page ID	1946702 (xsd:integer)
Wikipage revision ID	1111635755 (xsd:integer)
Link from a Wikipage to another Wikipage	Pseudo-differential operator Segal–Bargmann space José Enrique Moyal Phase-space formulation Connection (mathematics) Mathematics Matrix exponential Smooth function Fedosov manifold Phase space Symplectic manifold Baker–Campbell–Hausdorff formula Transformation between distributions in time–frequency analysis Weyl algebra Heisenberg group Darboux's theorem Differential operator Universal enveloping algebra Upper half-plane Hermann Weyl Hilbrand J. Groenewold Mathematical physics Symmetric algebra Theta representation Wigner–Weyl transform Poisson bracket Reduced Planck constant Kontsevich quantization formula Mathematical quantization Real numbers Moyal bracket Star product Heisenberg algebra Poisson bivector
sameAs	Moyal product Moyal product Moyal product Moyal product Moyal product
dbp:wikiPageUsesTemplate	dbt:About-distinguish2 dbt:Math dbt:Mvar dbt:Short_description
has abstract	Das Moyal-Produkt (nach José Enrique Moyal), auch Weyl–Groenewold-Produkt (nach Hermann Weyl und ), ist in der Mathematik eine zweistellige Verknüpfung auf dem Funktionenraum der glatten Funktionen über . Das assoziative, nicht-kommutative Produkt ist ein Spezialfall des Sternproduktes auf allgemeinen Poisson-Mannigfaltigkeiten. Das Moyal-Produkt ist eine „Deformierungsquantisierung“ einer linearen Poisson-Mannigfaltigkeit, das heißt, die Algebra der klassischen Observablen wird deformiert, sodass eine nicht-kommutative Algebra von Quanten-Observablen entsteht (Quantisierung). (de) In mathematics, the Moyal product (after José Enrique Moyal; also called the star product or Weyl–Groenewold product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space star product. It is an associative, non-commutative product, ★, on the functions on ℝ2n, equipped with its Poisson bracket (with a generalization to symplectic manifolds, described below). It is a special case of the ★-product of the "algebra of symbols" of a universal enveloping algebra. (en) Произведением Мояля — самый известный пример звёздного произведения в фазовом пространстве. Оно является ассоциативным коммутативным звёздного произведением функций на ℝ2n, оснащённым скобкой Пуассона (с обобщением на симплектические многообразия, см. ниже). Это особый случай звёздного произведения «алгебры символов» в универсальной обертывающей алгебре. Названо в честь израильского учёного Хосе Энрике Мояля. (ru)
prov:wasDerivedFrom	wikipedia-en:Moyal_product?oldid=1111635755&ns=0
page length (characters) of wiki page	9682 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Moyal_product
is Link from a Wikipage to another Wikipage of	Moyal José Enrique Moyal Phase-space formulation Uncertainty principle Commutator Geometric quantization Oscillator representation Stone–von Neumann theorem Phase space Weyl algebra Wigner quasiprobability distribution Universal enveloping algebra Hilbrand J. Groenewold Wigner–Weyl transform Kontsevich quantization formula Moyal bracket List of things named after Hermann Weyl Wehrl entropy Vasiliev equations Noncommutative geometry Noncommutative quantum field theory Phase-space wavefunctions Star product Star product (quantization)
is Wikipage redirect of	Star product (quantization)
is Wikipage disambiguates of	Moyal
is known for of	José Enrique Moyal Hilbrand J. Groenewold
is known for of	José Enrique Moyal Hilbrand J. Groenewold
is foaf:primaryTopic of	wikipedia-en:Moyal_product

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