Field theory reformulated without self-energy parts

The reformulation of field theory for avoiding self-energy parts in the dynamical evolution has been applied successfully for different systems. In the framework of the Lee model [de Haan, Exten. Ann. Phys. 311 (2004) 314] a kinetic extension of the description has been reached, enabling a statistical mixture to change its composition with time. The basic ingredient is the identification of these self-energy parts [de Haan and George, Trends in Stat. Phys. 3 (2000) 115]. The original reversible description is embedded in the new one and is recovered now from a restricted class of initial conditions [de Haan and George, Progr. Theor. Phys. 109 (2003) 881]. In the reduced formalism for a scalar field, interacting with a two-level atom, without the usual rotating wave approximation (RWA), the kinetic evolution operator, previously surmised [de Haan, Physica A 171 (1991) 159], has been derived from first principles, justifying the usual practice in optics. The model illustrates how some renormalization of the atomic levels (and vertices), through a dressing operator, finds its place naturally in the new formalism since the bare and dressed ground states no longer coincide. After dressing, the structure of the kinetic operators inside and outside the RWA is now common. Moreover, a finite velocity for field propagation is now possible, without the presence of precursors.