N.D. Cartwright: "A non-negative Wigner-type distribution", Physica 83A(1976) 210--212 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Classical Limit of Quantum Theory - Werner (1995) (Correct)
....on a special choice of, say, coherent states, unless there is a specific reason for considering a particular choice. One possible canonical choice of identifications is given in [We4] see (2) above) 6) infinitesimal h In the framework of nonstandard analysis [AFHL] the limit h 0 can be carried out simply by taking h literally infinitesimal. The art, as usual in this theory, is to extract from the resulting structure the relevant standard part . For the classical limit the idea is essentially taken from Theorem 8: the relevant observables for the classical limit are those, which ....
....spin in angular momentum units, which means that the half integer labelling the irreducible representation of SU 2 must go to infinity. This limit can be stated exactly along the lines of this paper, with analogous results. It is essentially equivalent to a mean field limit [GW] It can also be carried out for systems of many spins [RW] for more general compact Lie groups [Duf ] and for some quantum groups [GW] For a nonstandard version, see [WW] Acknowledgements This paper has grown out of a series of lectures given at the Marc Kac Seminar in Amsterdam in Summer 1993. The topic of ....
N.D. Cartwright: "A non-negative Wigner-type distribution", Physica 83A(1976) 210--212
Classical Mechanics as Quantum Mechanics with Infinitesimal h - Werner, Wolff (1995) (Correct)
....H = P 2 Q 2 ) 2 = Gamma h 2 Delta Q 2 ) 2. Then for any A 2 B(H) we define a function on phase space by (S A) hW ( Omega ; AW ( Omega i = h Omega ; ff Gamma (A) Omega i : 6) This is variously called the lower symbol [Sim] a smeared Wigner function [Car], the Husimi function [Tak] or the convolution with a coherent state [We1] of the operator A. In the other direction, we have the upper symbol [Sim] or P representation [KS] also going by many other names) which assigns an operator to each bounded measurable function f via S # f = Z dx dp ....
N.D. Cartwright:"A non-negative Wigner-type distribution", Physica 83A(1976) 210-212
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