Moyal brackets, star products and the generalised Wigner function
نویسندگان
چکیده
منابع مشابه
Moyal Brackets, Star Products and the Generalised Wigner Function
The Wigner-WeylMoyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space co-ordinate, for example, in terms of a bilinear convolution of two fermionic objects, e.g. a quark antiquark pair. This construction is essentially non-local,...
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We give a q-analysis version of a discretization procedure of Kemmoku and Saito leading to an apparently new q-Moyal type bracket. 2000 Mathematics Subject Classification. 81R50, 81S30.
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The infinite limit of Matrix Theory in 4 and 10 dimensions is described in terms of Moyal Brackets. In those dimensions there exists a Bogomolni’y bound to the Euclideanized version of these equations, which guarantees that solutions of the first order equations also solve the second order Matrix Theory equations. A general construction of such solutions in terms of a representation of the targ...
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We regard classical phase space as a generalised complex manifold and analyse the B–transformation properties of the ⋆–product of functions. The C–algebra of smooth functions transforms in the expected way, while the C–algebra of holomorphic functions (when it exists) transforms nontrivially. The B–transformed ⋆–product encodes all the properties of phase–space quantum mechanics in the presence...
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We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a deformation of the classical phase-space: instead of being a vector space it becomes a manifold, the topology of which is given by the commutator relations. It ...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 1999
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(98)00158-1