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.

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.

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1. Dynamic symmetry breaking is a nonperturbative process; therefore, to solve the Schwinger-Dyson equations to study this process, methods other than those based on perturbation theory are required. Thus, in [1][2][3][4] it was revealed that already in the simplest nonperturbative ladder approach for the electron propagator in QED 4 , an originally massless electron acquires a dynamic mass when the coupling constant exceeds its critical value. More recently, it has been demonstrated that the main features of the phenomenon established in the ladder approximation are also retained beyond its limits [5].The similar situation is also typical of QED 3 , except the absence of the parameter whose threshold value would indicate the phase transition accompanied by dynamic chiral symmetry breaking. On the other hand, an interesting and, apparently, far-reaching analogy between QED 4 at a nonzero temperature (with the temperature being the parameter of ultraviolet cutoff) and QED 3 (with the corresponding parameter at zero temperature) has recently been established [6]. This circumstance stimulates a more detailed study of the above-indicated model to establish the presence of the abovementioned transition and the corresponding threshold parameter.2. We proceed from the Schwinger-Dyson equation for the fermion mass function in the ladder approximation with the Landau gauge for the photon propagator. We have [1,2]