Particles Interacting with a Boson Field

  • Luigi Accardi
  • Igor Volovich
  • Yun Gang Lu


In the general scheme of interaction, described in Sect. 4.8, the techniques described in Part I do not apply to the case when not only the reservoir R but also the system S has a continuous spectrum. The usual way to handle these more complex interactions consists in replacing the response term by the first few terms in its series expansion. For example, in the case of nonrelativistic quantum electrodynamics (QED) (e.g. in nonlinear optics, laser theory, etc.) this amounts to replacing the dipole approximation by a multipole expansion. These approximations however break momentum conservation, and we shall see that by introducing them one loses information on some subtle cancella- tions which occur due to fast oscillations.


Commutation Relation Stochastic Differential Equation Canonical Commutation Relation Hilbert Module Stochastic Limit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luigi Accardi
    • 1
  • Igor Volovich
    • 2
  • Yun Gang Lu
    • 3
  1. 1.Centro Vito Volterra, Facolta di EconomiaUniversità di RomaRomaItaly
  2. 2.Steklov Mathematical InstituteMoscow, GSP-1Russia
  3. 3.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly

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