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.


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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