About the chiral symmetry breaking in QED3

Abstract

The problem of the chiral symmetry breaking in QED 3 is considered by solving the Schwinger-Dyson equation for the fermion propagator in the ladder approximation using the Landau gauge for the photon propagator. Within the framework of the indicated approximation, different simplifications that allow expressions for the fermion mass function to be retrieved in an explicit form are analyzed. The results obtained are compared with the data of numerical analysis. It appears that the neglect of higher Gegenbauer harmonics in the kernel of the initial integral equation for the fermion mass function influences the dynamic mass value and the asymptotics of the mass function only weakly. On the other hand, it is established that the conclusion about a complicated structure of the fermion vacuum of the massive phase is an artifact of linearization of the Schwinger-Dyson equation kernel: consideration of the kernel nonlinearity yields a simple massive phase structure of the fermion vacuum.1. Quantum electrodynamics in three-dimensional space (QED 3 ) has long drawn attention of many researchers. First, it is one of the few renormalizable theories. Second, the chiral symmetry braking takes place here [1-3] together with the spatial and temporal parities [4]. Third, confinement is observed in QED 3 for some approximations [5][6][7][8], which allows this phenomenon to be studied in more details compared to the QCD because of a simpler model. There are also grounds to believe that progress will be made in understanding of some macroscopic effects, in particular, hightemperature superconductivity. QED 3 is used to a certain degree to explain the structure of the elementary fermion excitation spectrum of the recently discovered layered structure -graphene [9, 10].In the present work, the problem of the chiral symmetry breaking in QED 3 is considered. Comparing from this point of view QED 3 and QED 4 , we note that there are no dimensional parameters in the latter that can be used to express the particle mass. Therefore, the dynamic mass arising here due to the chiral symmetry breaking is proportional to the cutoff parameter [11][12][13][14]. In QED 3 , there is such parameter. On the other hand, in the context of the perturbation theory, the integral of the fermion energy in QED 3 diverges logarithmically, which suggests that the dynamic mass can be expressed through the cutoff parameter as well. Thus, the scale competition takes place in QED 3 , and the question arises about momentum values that play the main role in the chiral symmetry breaking.The 4-component QED 3 representation is considered below. The Schwinger-Dyson equations that must be solved by a non-perturbative method are used to analyze the symmetry breaking. Thus, the chiral symmetry breaking in QED 4 is observed already in the simplest non-perturbative ladder approximation if the coupling constant exceeds a critical value [11][12][13][14]. In this case, there exists a close analogy between the phenomena of incidence in the center in a strong Coulomb field for the...