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Existence of the limiting mean field dynamics in general equilibrium representations

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  • Duffner, Eberhard

Abstract

The existence of the limiting finite time transformations is proved for a class of discrete mean field models in all states, which are asymptotically permutation invariant. To this end detailed approximation and analyticity properties of the complex many-time Green's functions are worked out. For a rather general class of grand canonical equilibrium states the limiting time transformations are shown to constitute a W∗-automorphism group in the corresponding GNS-von Neumann algebra in spite of the extremely long-range interaction potential and in spite of the center not necessarily being point-wise invariant. Approximation properties for the finite temperature Heisenberg generators are obtained by complex differentiation.

Suggested Citation

  • Duffner, Eberhard, 1985. "Existence of the limiting mean field dynamics in general equilibrium representations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(1), pages 187-212.
    • Handle: RePEc:eee:phsmap:v:133:y:1985:i:1:p:187-212
    DOI: 10.1016/0378-4371(85)90063-9
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    1. Barend A. De Vries, 1972. "International Price Comparisons of Selected Capital Goods Industries," NBER Chapters, in: International Comparisons of Prices and Output, pages 335-367, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Honegger, Reinhard, 1996. "The weakly coupled infinite Dicke model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 391-411.

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