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Field Theory reformulated without Self-energy Parts. The dressing Operator
The reformulation of field theory for avoiding self-energy parts in the
dynamical evolution has been applied successfully in the framework of the Lee
model, [M. de Haan. Ann. Phys., 311, 314-349 (2004)] enabling a kinetic
extension of the description. The basic ingredient is the recognition of these
self-energy parts. [M. de Haan and C. George. Trends in Statistical Physics 3
(2000), 115] The original reversible description is embedded in the new one and
appears now as a restricted class of initial conditions. [M. de Haan and C.
George. Prog. Theor. Phys.,109, 881-909 (2003)] This program is realized here
in the reduced formalism for a scalar field, interacting with a two-level atom,
beyond the usual rotating wave approximation. The kinetic evolution operator,
previously surmised, [M. de Haan. Physica, A171 (1991), 159] is here derived
from first principles, justifying the usual practice in optics where the common
use of the so-called pole approximation should no longer be viewed as an
approximation but as an alternative description in the appropriate formalism.
That model illustrates how some dressing of the atomic levels (and vertices),
through an appropriate operator, finds its place naturally into the new
formalism since the bare and dressed ground states do no longer coincide.
Moreover, finite velocity for field propagation is now possible in all cases,
without the presence of precursors for multiple detections.Comment: 55 pages. Revised version for Annals of Physics. Typos and English
corrections, references and precisions adde