Abstract
Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation, performed entirely in momentum space, shows the complete agreement between nonperturbative and perturbative approaches.
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It is worthy noting that the iteration equation (4.7) of [36] is a kind of Dyson-Schwinger equation which follows from the very construction of the diagram on Fig. 4, where 2n-th vertex is fixed. It is also reflected by the presence of p + on the left hand side of (4.8). This gives in fact the expansion of the derivative of S (in coordinate space), as also seen in (4.10), whereas our equation (15) gives the expansion of S itself. Of course both approaches are equivalent.
I.S. Gradshteyn’s, I.M. Ryzhik’s, Table of Integrals Series and Products (Academic Press, New York 1980)
K. Stam, J. Phys. G: Nucl. Phys. 9, L229 (1983). Please note the slight disagreement in coefficient
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Radozycki, T. Summing up the perturbation series in the Schwinger Model. Eur. Phys. J. C 6, 549–553 (1999). https://doi.org/10.1007/s100529800933
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DOI: https://doi.org/10.1007/s100529800933