Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED - art. no. 065007

In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. I n D < 4 dimensions the theory has solutions which exhibit chiral symmetry b reaking for all values of the coupling. To begin with, we study this phenom enon both numerically and, with some approximations, analytically within th e rainbow approximation in the Landau gauge. In particular, we discuss how to extract the critical coupling alpha(c) = pi/3 relevant in 4 dimensions f rom the D dimensional theory. We further present analytic results for the c hirally symmetric solution obtained with the Curtis-Pennington vertex as we ll as numerical results for solutions exhibiting chiral symmetry breaking. For these we demonstrate that, using dimensional regularization, the extrac tion of the critical coupling relevant for this vertex is feasible. Initial results for this critical coupling are in agreement with cut-off based wor k within the currently achievable numerical precision. [S0556-2821(99)06916 -7].