| Popis: |
Under the global title "The non triviality of a Φ 4 4 model" we show in the form of three separate articles "I', "II", "III", the existence and uniqueness of a solution to a Φ 4 4 non linear renormalized system of equations of motion in Euclidean space. This system represents a non trivial model which describes the dynamics of the Φ 4 4 Green's functions in the Wightman Axiomatic Quantum Field Theory (AQFT) framework. The work constitutes the extension in 4-dimensions of a previous theoretical and numerical study, in zero dimensional space, by application of a fixed point theorem to another equivalent form of this dynamic system the so called Φ 4 0 "new mapping" M * which has been shown to be locally con-tractive, something verified by the numerical results. This extension, called "new Φ 4 4 mapping M * " is locally contractive inside a neighborhood of a particular "tree type" sequence of renormalized Green 's functions, in the four dimensional euclidean momentum space. This neighborhood (and the Φ 4 4 non trivial solution), belongs to a particular subset of the appropriate Banach space characterized by precise "renormalization physical parame-ters" "alternating signs", "splitting", "linear (AQFT) properties" and "good asymptotic behaviour" with respect to the four-dimensional Euclidean external momenta. |
