Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2002-09-04
JHEP 0302 (2003) 001
Physics
High Energy Physics
High Energy Physics - Phenomenology
JHEP style, 35 pages, 12 figures, text culturer improves, typos corrected, results and references unchanged
Scientific paper
10.1088/1126-6708/2003/02/001
Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with massive pseudoscalar meson and conventional spinor QED. Within the momentum subtraction procedure, the appropriate renormalization is performed analytically which leads to the usual dispersion formulation. The electron propagator obtained in this frame is compared with the solution of Euclidean Dyson-Schwinger equation and with the perturbation theory results as well. The proposed method has the advantage of obtaining solutions in both the space- and {\bf{time}}-like regimes of momenta. In addition,when the coupling constant increases we find some un-expected discrepancy between the Euclidean and integral representation solutions. Especially, when the solutions of the original momentum DSE's exhibit the signal for confinement then the spectral approach gives no solution for Lehmann function of confined particle.
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