Existence of the limiting mean field dynamics in general equilibrium representations

Eberhard Duffner

Physica A: Statistical Mechanics and its Applications, 1985, vol. 133, issue 1, 187-212

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.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:133:y:1985:i:1:p:187-212

DOI: 10.1016/0378-4371(85)90063-9

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