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

Hirokawa, Masao

J. Math. Soc. Japan 51, No. 2, 337-369 (1999).

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

Keywords:

inverse problem; quantum field theory; finite temperature; infinite volume limit; rotating wave approximation; quantum harmonic oscillator in thermal equilibrium; canonical correlation function