The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit, already obtained by Noja and Posilicano [Ann. I.H.P. Phys. Theor. 71, 425 (1999)], is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behavior of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behavior is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibits in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator. (c) 2005 American Institute of Physics.

Bertini, M., Noja, D., Posilicano, A. (2005). Rigorous dynamics and radiation theory for a Pauli-Fierz model in the ultraviolet limit. JOURNAL OF MATHEMATICAL PHYSICS, 46(10) [10.1063/1.2009607].

Rigorous dynamics and radiation theory for a Pauli-Fierz model in the ultraviolet limit

NOJA, DIEGO DAVIDE;
2005

Abstract

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit, already obtained by Noja and Posilicano [Ann. I.H.P. Phys. Theor. 71, 425 (1999)], is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behavior of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behavior is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibits in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator. (c) 2005 American Institute of Physics.
Articolo in rivista - Articolo scientifico
pauli-fierz model; ultraviolet limit; point interactions;
English
2005
46
10
102305
reserved
Bertini, M., Noja, D., Posilicano, A. (2005). Rigorous dynamics and radiation theory for a Pauli-Fierz model in the ultraviolet limit. JOURNAL OF MATHEMATICAL PHYSICS, 46(10) [10.1063/1.2009607].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1960
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