The dynamical generation of a fermion mass is studied within (2 + 1)-dimensional QED with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, Nc. It is found that the dynamical fermion mass appears for N < Nc where Nc = 3.29, that is only about 1% larger than its value at leading order.

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The Bound State in QED is described in systematic way by means of nonlocal irreducible representations of the nonhomogeneous Poincare group and Dirac's method of quantization. As an example of application of this method we calculate triangle diagram P ara − P ositronium → γγ. We show that the Hamiltonian approach to Bound State in QED leads to anomaly-type contribution to creation of pair of parapositronium by two photon.

The low energy Gell-Mann-Oakes-Renner relation, Higgs particle mass value, and the new observational cosmological data are considered as evidence of the condensate mechanism of conformal symmetry breaking at the quantum level. The condensate mechanism occurs by means of normal ordering of field operators in QCD, Minimal Standard Model of electroweak interactions without the Higgs potential, and the Dirac conformal General Relativity with long range forces.