  The Schwinger--Dyson equations (SDEs) are coupled integral equations for the
Green's functions of a quantum field theory (QFT). The SDE approach is the
analytic nonperturbative method for solving strongly coupled QFTs. When applied
to QCD, this approach, also based on the first principle, is the analytic
alternative to lattice QCD. However, the SDEs for the n-point Green's functions
involves (n+1)-point Green's functions (sometimes (n+2)-point functions as
well). Therefore any practical method for solving this infinitely coupled
system of equations requires a truncation scheme. When considering strongly
coupled QED as a modeling of QCD, naive truncation schemes violate various
principles of the gauge theory. These principles include gauge invariance,
gauge covariance, and multiplicative renormalizability. The combination of
dimensional regularization with the spectral representation of propagators
results in a tractable formulation of a truncation scheme for the SDEs of QED
propagators, which has the potential to preserve the aforementioned principles
and renders solutions obtainable in the Minkowski space.
