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.
Reviewer: A.N.Kochubei (Kyïv)
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 |