No abstract

The potential of a point source placed on a flat surface is calculated in the context of reduced QED 3+1 , and the effective charge behavior is investigated with allowance for the polarization of vacuum. Both approximate analytical and numerical methods are used in calculations. It is established that the behavior of the examined potential at short and long distances from the source does not deviate significantly from the Coulomb behavior of vacuum massless and massive fermions. Other deviations of the results obtained from the well-known standard QED 3+1 and QED 2+1 data are also discussed.

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...

Dynamic mass generation in 3D quantum electrodynamics (QED 3 ) is considered at T ≠ 0. To solve the Schwinger-Dyson equation for the Matsubara electron Green's function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED 3 at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED 3 , at T = 0 in QED 4 , and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger-Dyson equation are of the same orders of magnitude.Three-dimensional quantum electrodynamics at T ≠ 0 attracts more and more attention for some reasons. First, dynamical breaking of chiral symmetry that leads to mass generation for an initially massless particle is observed here [1]. Second, under certain conditions, confinement is present in QED 3 , and due to comparative simplicity of the model, this phenomenon can be investigated in more detail than in quantum chromodynamics (QCD) [2,3]. Moreover, definite analogy between QED 3 and graphene physics exists [4].In the present work, dynamical breaking of the chiral symmetry is investigated in the QED 3 at T ≠ 0 and the phase transition which accompanies this process and the subsequent restoration of the initial symmetry are studied. In this case, the Schwinger-Dyson equation for the Green's temperature function of a fermion in the ladder approximation with additional restrictions on the Green's photonic function is used in the Landau gauge and instant approximation.

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED3 is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED 3 , complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.