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Study of the Schwinger-Dyson equation (SDE) for the fermion propagator to obtain dynamically generated chirally asymmetric solution in any covariant gauge is a complicated numerical exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the SDE for every value of the gauge parameter. Starting from the Landau gauge where the computational complications are still manageable, we apply the Landau-Khalatnikov-Fradkin tansformation (LKFT) on the dynamically generated solution and find approximate analytical results for arbitrary value of the covariant gauge parameter. We also compare our results with exact numerical solutions.

How to solve the Schwinger-Dyson equations once and for all gauges