SELF-CONSISTENT SOLUTION OF THE SIMULTANEOUS SCHWINGER-DYSON EQUATION IN STRONG COUPLING QED

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Abstract
In the strong coupling region of QED, we have obtained a numerical solution to the simultaneous Schwinger-Dyson equation for the fermion and the photon propagators. It is shown that there is a critical point separating the spontaneous-chiral-symmetry-breaking (strong coupling) phase and the weak coupling phase. This critical point is consistently interpreted as the second order phase transition point at which the continuum limit of cutoff QED may be taken. The vacuum polarization function obtained in this framework exhibits essentially the same asymptotic uv behavior as that predicted from the one-loop calculation. The scaling behavior is not inconsistent with the mean-field result as predicted from the one-loop case, which favors the triviality of QED.

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