M.A. Rieffel: "The classical limit of dynamics for spaces quantized by an action of IR d ", Preliminary version, March 1995  Home/Search   Document Not in Database   Summary   Related Articles

.... of compact support have been made the basis of a discussion of the classical limit by Emch [Em1,Em2] In his approach each classical observable F 0 thus has a unique h sequence of quantum observables F h associated with it, which is also typical for deformation quantization approaches [Ri1,Ri2,Ri3] In our approach this constraint becomes unnecessary, both from a technical and from a conceptual point of view. Emch s main emphasis is on defining the (weak) convergence of states with respect to this particular set of sequences. The intersection between his classical states , and our ....

....time evolution exists for all times, so some restrictions on H h are always needed. A good way of handling unbounded Hamiltonians is also to study the dynamics in the norm limit of states (see (2) and [Hep,Hag] In the deformation quantization approach, dynamics was recently discussed in [Ri3] 4) Classical trajectories The Evolution Theorem does not explain how, in the classical limit, a description of the systems in terms of trajectories becomes possible. The statistics of trajectories 28 should be the limit of a sequence of continual measurement processes depending on h. One ....

M.A. Rieffel: "The classical limit of dynamics for spaces quantized by an action of IR d ", Preliminary version, March 1995

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