An inverse problem in quantum field theory and canonical correlation functions.(English)Zbl 0927.46055

We treat a quantum harmonic oscillator in thermal equilibrium with any systems in certain classes of bosons with infinitely many degrees of freedom. We describe the following results:
(i) when a canonical correlation function is given, we so reconstruct a Hamiltonian by the rotating wave approximation from it that the Hamiltonian restores it. Namely, we solve an inverse problem in the quantum field theory at finite temperature in a finite volume.
(ii) Taking an infinite volume limit for the result in (i), we consider long-time behavior of the canonical correlation function in the infinite volume limit.

MSC:

 46N50 Applications of functional analysis in quantum physics 82B10 Quantum equilibrium statistical mechanics (general) 47L60 Algebras of unbounded operators; partial algebras of operators 47N50 Applications of operator theory in the physical sciences 47N55 Applications of operator theory in statistical physics (MSC2000) 82C22 Interacting particle systems in time-dependent statistical mechanics
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