Expansion parameter of the vertex function in the two-dimensional approximation of quantum electrodynamics

The contribution of the fifth-order diagrams to the vertex function of an electron in a strong magnetic field B B₀ = m²/e = 4.41·10¹³ G is calculated. It is shown that the diagram with electron loop is dominant; this leads to a linear dependence of the form factor f⁽⁵⁾(t) on the field. Comparison with the main contribution from the simplest triangle diagram shows that perturbation theory in. becomes invalid in fields with induction 10^17–18 G.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 126–129, September, 1978.