Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-12-14
Few Body Syst.39:45,2006
Physics
High Energy Physics
High Energy Physics - Phenomenology
57 pages, Sections slightly reorganized, one section devoted to CHSB added, references changed, accepted in Few-body Systems
Scientific paper
10.1007/s00601-006-0156-0
We review some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral representation in QFT and a discussion of renormalization in this approach. The technique based on the integral representation of Green's functions is exploited to solve Schwinger-Dyson equations in several quantum field models, eg. in scalar models and in strong coupling $QED_{3+1}$ in the quenched and in the unquenched approximation. The phenomenon of dynamical chiral symmetry breaking in regularized theory is touched. In QCD, the analyticity of gluon propagator on the complex momentum square plane is exploited to continue some recent lattice data to timelike momentum axis. We find non-positive absorptive part contribution in the Landau gauge gluon propagator which is in agreement with some other new recent analyzes.
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