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A formalism of gauge and Lorentz covariant Schwinger-Dyson equation is builtup for fermion propagator in presence of arbitrary external gauge field withinladder approximation. Different type external electromagnetic field dependenttrial solutions are investigated which spontaneously breaking chiral symmetry.Comment: 10 page

Gauge Covariant Fermion Propagator in the Presence of Arbitrary External Gauge Field and Its Schwinger–Dyson Equation