Abstract
We present recently obtained results for dynamical chiral symmetry breaking studied within (2 + 1)-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1/N expansion are computed exactly in an arbitrary non-local gauge.
Highlights
In these Proceedings we present the results of our recent papers [1, 2], where the critical behavior of Quantum Electrodynamics in 2 + 1 dimensions (QED3) has been studied
Dynamical chiral symmetry breaking (DχSB) in QED3 and the dependence of the dynamical fermion mass on N have been the subject of extensive studies, see, e.g., [1, 2, 4,5,6,7,8,9,10,11,12,13]
We have presented the studies [1, 2] of DχSB in QED3 by including 1/N2 corrections to the SD equation exactly and taking into account the full ξ-dependence of the gap equation
Summary
In these Proceedings we present the results of our recent papers [1, 2], where the critical behavior of Quantum Electrodynamics in 2 + 1 dimensions (QED3) has been studied. In [2], the results of [1] were generalized to an arbitrary non-local gauge [15] It was shown in [2] that a resummation of the wave-function renormalization yields a strong suppression of the gauge dependence of the critical fermion flavour number, Nc(ξ) where ξ is the gauge fixing parameter, which is such that DχSB takes place for N < Nc(ξ). It is found that: Nc(1) = 3.0084 in the Feynman gauge, Nc(0) = 3.0844 in the Landau gauge and Nc(2/3) = 3.0377 in the ξ = 2/3 gauge where the leading order fermion wave function is finite These results suggest that DχSB should take place for integer values N ≤ 3. It is the purpose of this work to review some of the basic steps of papers [1, 2] which represent an essential improvement with respect to Nash’s approximate NLO results derived some 30 years ago
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