arXiv subjects
Publications and source records attributed to V. Sauli.
This is an abstract of authors PhD thesis which is devoted to studies of quantum field models with strong coupling. The {\em Schwinger-Dyson equations} (SDEs) in momentum representation are solved in Minkowski space. The original version of the paper hep-ph/0108160 is included in. The full text of author's PhD thesis can be found at this WWW: 'http://gemma.ujf.cas.cz/~sauli/papers.html'
The loop structure of two point Green's functions is investigated in the Wess-Zumino model in the formalism where the auxiliary fields are integrated out. In the usual frame of perturbation theory the deviation from the non-renormalization theorem is explicitly shown. It is shown that Ward identity are not satisfied in this approach. Further we go beyond perturbation theory by solving a system of regularized Schwinger-Dyson equations (SDEs). The mass splitting between fermions and bosons, which was already observed in perturbation theory level, is further enhanced.
Schwinger-Dyson equations for propagators are solved for the scalar $Φ^3$ theory and massive Wick-Cutkosky model. With the help of integral representation the results are obtained directly in Minkowski space in and beyond bare vertex approximation. Various renormalization scheme are employed which differ by the finite strength field renormalization function $Z$ . The $S-$matrix is puzzled from the Green's function and the effect of truncation of the DSEs is studied. Independently on the approximation the numerical solution breaks down for certain critical value of the coupling constant, for which the on-shell renormalized propagator starts to develop the unphysical singularity at very high space-like square of momenta.
The Schwinger-Dyson equation for a scalar propagator is solved in Minkowski space with the help of an integral spectral representation, both for spacelike and timelike momenta. The equation is re-written into a form suitable for numerical solution by iterations. This procedure is described for a simple unphysical Lagrangian with a cubic interaction, with future extensions to more realistic theories in mind.