Poisson bracket

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• Poisson bracket — In mathematics and classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition of the time evolution of a dynamical system in the Hamiltonian formulation. In a more general… …   Wikipedia

• Bracket (disambiguation) — Bracket may refer to: * Bracket, one of a class of punctuation marks used in pairs to set apart or interject text within other text ** Square bracket, one type of punctuation bracket (primarily American usage) ** Parenthesis, another type of… …   Wikipedia

• Poisson manifold — In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra. Since their introduction by André… …   Wikipedia

• Poisson algebra — In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central… …   Wikipedia

• Poisson ring — In mathematics, a Poisson ring A is a commutative ring on which a binary operation [,] , known as the Poisson bracket, is defined. Many important operations and results of symplectic geometry and Hamiltonian mechanics may be formulated in terms… …   Wikipedia

• Bracket — 〈 redirects here. It is not to be confused with く, a Japanese kana. This article is about bracketing punctuation marks. For other uses, see Bracket (disambiguation). Due to technical restrictions, titles like :) redirect here. For typographical… …   Wikipedia

• Bracket (mathematics) — In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses ( ), square brackets [ ] , curly brackets { }, and angle brackets < >. In the typical use, a mathematical expression is… …   Wikipedia

• Dirac bracket — The Dirac bracket is a generalization of the Poisson bracket developed by Paul Dirac to correctly treat systems with second class constraints in Hamiltonian mechanics and canonical quantization. It is an important part of Dirac s development of… …   Wikipedia

• Moyal bracket — In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase space star product. The Moyal Bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a… …   Wikipedia

• Schouten-Nijenhuis bracket — In differential geometry, the Schouten Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different… …   Wikipedia

• Schouten–Nijenhuis bracket — In differential geometry, the Schouten–Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different… …   Wikipedia