Field theory reformulated without self-energy parts. Kinetic extension for the Lee model

An alternative formulation of field theory is possible such that self-energy contributions do no longer appear as dynamical processes. The dynamics is now described by kinetic-like equations of motion, involving more degrees of freedom than in the original formulation, plus a constraint propagating in time. Considering situations outside the equivalence conditions provides a natural irreversible extension of quantum field. The relevance of such extension relies on the positivity and normalization of the extension. The feasibility is examplified here on the Lee model without focusing on a particular sector. The tool used is the single subdynamics approach [Trends Stat. Phys. 3 (2000) 115]. A partial treatment of the Lee model along those lines have been considered for a particular sector [Prog. Theor. Phys. 109 (2003) 881]. We intend to consider here a set of sectors using a reduction formalism [Physica A 171 (1991) 159] which provides directly the required properties. Outside the equivalence conditions, our approach couples sectors and the resulting statistical mixture changes its composition with time