Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-11-20
Phys.Rev.D60:065007,1999
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, including 5 figures; submitted to Phys. Rev. D
Scientific paper
10.1103/PhysRevD.60.065007
In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. In D < 4 dimensions the theory has solutions which exhibit chiral symmetry breaking for all values of the coupling. To begin with, we study this phenomenon both numerically and, with some approximations, analytically within the rainbow approximation in the Landau gauge. In particular, we discuss how to extract the critical coupling alpha_c = pi/3 relevant in four dimensions from the D dimensional theory. We further present analytic results for the chirally symmetric solution obtained with the Curtis-Pennington vertex as well as numerical results for solutions exhibiting chiral symmetry breaking. For these we demonstrate that, using dimensional regularization, the extraction of the critical coupling relevant for this vertex is feasible. Initial results for this critical coupling are in agreement with cut-off based work within the currently achievable numerical precision.
Gusynin Valery P.
Schreiber Andreas W.
Sizer Tom
Williams Anthony G.
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