Friedrichs model with virtual transitions. Exact solution and indirect spectroscopy. (English) Zbl 1046.81075

Summary: The Friedrichs-type model of interaction between matter (multilevel system) and radiation including virtual transitions is considered. The canonical Bogolubov transformation diagonalizing the total Hamiltonian is constructed. It is pointed out that the transformation is improper when the discrete part of the spectrum of system is “dissolved” in the continuous one. The new vacuum state for the total Hamiltonian is obtained. The time evolution of the bare vacuum and the bare operators is calculated. Using the exact solution, the result of R. Passante, T. Petrosky, and I. Prigogine [Physica A 218, 437 ff (1995)] that the transition from the bare vacuum state to the true vacuum leads to the emission of real photons is confirmed. The dressing of the bare vacuum at the presence of resonances is an irreversible process. The relation of the result with the idea of “indirect spectroscopy” is discussed.


81T10 Model quantum field theories
81V80 Quantum optics
81U15 Exactly and quasi-solvable systems arising in quantum theory
Full Text: DOI


[1] Passante R., Physica A 218 pp 437– (1995)
[2] DOI: 10.1016/0378-4371(93)90047-8
[3] Petrosky T., Physica A 173 pp 242– (1991)
[4] Petrosky T., Phys. Lett. A 164 pp 379– (1992)
[5] Pavlov B. S., St. Petersburg Math. J. 4 pp 1245– (1993)
[6] Antoniou I., Comput. Math. Appl. 34 pp 425– (1997)
[7] Antoniou I. E., J. Math. Phys. 39 pp 2459– (1998) · Zbl 1001.81084
[8] Antoniou I., J. Math. Phys. 39 pp 2995– (1998) · Zbl 1006.47055
[9] DOI: 10.1063/1.524871
[10] DOI: 10.1016/0960-0779(94)90050-7 · Zbl 0799.58074
[11] Petrosky T., Chaos Solitons Fractals 7 pp 441– (1996) · Zbl 1080.82550
[12] Petrosky T., Adv. Chem. Phys. pp 1– (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.