Theory of radiation reaction and atom self-energies: an operator reaction field

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Abstract
The field generalizes in a natural way the c-number theory of radiation reaction and frequency shifts due to Lorentz. By a trivial extension the operator field can be applied to the more complicated cases of a single multi-level atom and the super-radiant problem of N atoms on the same site where these are coupled either to the vacuum or the vacuum and additional imposed quantized fields. By further extension it also applies to the case of N atoms on different sites. Explicit expressions for positive and negative frequency parts of the total operator field are given in terms of arbitrary dipole operator sources and are apparently valid for times t>> omega s-1>> omega max-1 where omega s is the atomic resonance and omega max a cut-off used systematically throughout the theory.