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Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansion. (English) Zbl 0932.82013

The authors introduce a definition of an Euclidean Gibbs state corresponding to continuous systems of quantum particles with Boltzmann statistics. The interaction is described by a pair potential \(v(x-x')\). Under the assumption that \(v\) is an absolutely integrable function, it is shown that the set of such Euclidean Gibbs states is not empty at least for sufficiently small values of the inverse temperature. The proof is based on the method of cluster expansions of the Brydges-Federbush type.

MSC:

82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
82B10 Quantum equilibrium statistical mechanics (general)
46N55 Applications of functional analysis in statistical physics