Abstract
In the case of nonzero fermion mass, within a range of Ansatze for the full fermion-boson vertex, we show that Dyson-Schwinger equation for the fermion propagator in QED3 has two qualitatively distinct dynamical chiral symmetry breaking solutions. As the fermion mass increases and reaches to a critical value mc, one solution disappears, and the dependence of mc on the number of fermion flavors is also given.
Highlights
Nowadays, it is widely accepted that Quantum Chromodynamics (QCD) in 3 + 1 dimensions is the fundamental theory for strong interaction
In the case of nonzero fermion mass, within a range of Ansätze for the full fermion-boson vertex, we show that Dyson-Schwinger equation for the fermion propagator in QED3 has two qualitatively distinct dynamical chiral symmetry breaking solutions
It is widely accepted that Quantum Chromodynamics (QCD) in 3 + 1 dimensions is the fundamental theory for strong interaction
Summary
It is widely accepted that Quantum Chromodynamics (QCD) in 3 + 1 dimensions is the fundamental theory for strong interaction. When the current quark mass m is nonzero, the quark gap equation has only one solution which corresponds to the NG phase and the solution corresponding to the WN phase does not exist [1,2]. This conclusion is hard to understand and one will naturally ask why the Wigner solution of the quark gap equation only exists in the chiral limit and does not exist at finite current quark mass. [3] first discussed this problem and asked whether the quark gap equation has a Wigner solution in the case of nonzero current quark mass. In the present paper we try to propose a new approach to investigate this problem in the framework of a relatively simple Abelian toy model of QCD, namely, quantum electrodynamics in 2 + 1 dimensions (QED3)
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