An example of a Kubo–Martin–Schwinger state for a nonlinear classical poisson system with infinite-dimensional phase space

A. A. Arsen'ev


Abstract: A “smoothed” nonlinear Klein–Gordon equation is regarded as the equation of evolution of a classical dynamical system with an infinite-dimensional phase space. It is proved that the wave operators are canonical transformations of this system that linearize it. It is shown that a Gaussian measure induces a Kubo–Martin–Schwinger state for the linear system, and that the preimage of this measure under the canonical transformation implemented by a wave operator is a Kubo–Martin–Schwinger state for the original nonlinear system.
Bibliography: 8 titles.

UDC: 517.9

MSC: Primary 58F05; Secondary 47L30, 58D25, 70G35, 76F99, 81C05

Received: 14.01.1980

 English version: Mathematics of the USSR-Sbornik, 1982, 43:1, 103–115

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