Particles Interacting with a Boson Field
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.
KeywordsCommutation Relation Stochastic Differential Equation Canonical Commutation Relation Hilbert Module Stochastic Limit
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