One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinor-bilinear scalar density has no mixed couplings of A-V form. On the other hand, the space-time dimensionality cannot be constrained from multidimensional phenomenological models admitting torsion.

We provide a new insight into the problem of generating the hadron mass spectrum in the framework of the covariant confined quark model. One of the underlying principles of this model is the compositeness condition (CC) which puts equal to zero the renormalization constant of the bare hadron wave function. In particular, this equation allows us to express the Yukawa coupling $g$ of the meson fields to the constituent quarks as a function of other model parameters. In addition to the CC we also employ another equation relating the meson mass function to the Fermi coupling $G$. Both equations guarantee that the Yukawa-type theory is equivalent to the Fermi-type theory thereby providing an interpretation of the meson field as the bound state of its constituent fermions (quarks). We evaluate the Fermi-coupling as a function of meson (pseudoscalar and vector) mass $M_J$ and obtain a smooth behavior $G(M_J)$ by varying $M_J$. The meson mass spectrum obtained in this manner is found in good agreement with the experimental data. We also compare the behavior of our Fermi coupling with the strong QCD coupling $\alpha_s$ calculated earlier within an QCD-inspired approach.

The behavior of quantum particle in a stochastic environment is described by Green function in a functional integral representation and some methods of its evaluation are proposed. The localization length is calculated in the case of movement in unordered environment and in the environment which is described by stochastic potential of Gauss type. The movement of a quantum particle in a vacuum of quantized field is considered. The difference between non-relativistic and relativistic approaches is shown.

The density matrix of charged relativistic fermion in the homogenous constant magnetic field was obtained. With the use of density matrix expression in momentum space the technic of calculation of quantum processes with charged fermions in the external field was considered. By using this technic the neutrino luminosities in the reactions of annihilation of electron and positron into a pair of neutrino and the reactions of neutrino synchrotron radiation by the electron (positron) were calculated. It was shown that the results of the calculation are in agreement with the known ones from the literature. Obtained results can be used for modeling of giant flashes on the neutron stars - the sources of soft gamma repeaters (SGR).

In this work two approaches were considered for the description of transitions of $K^o$, $\bar K^o$ mesons into $K^o_1$ ($K_S$) mesons in $CP$ violation in weak interactions. First approach uses the standard theory of oscillations. Second one assumes that $K_S$, $K_L$ states, which appear in $CP$ violation, are normalized, but not the orthogonal functions of states. In this case not the oscillations take place but the interference between these states. It is noted that the existing experimental data are in a good agreement with the second approach with $\sin^2 \beta = 2.23 \cdot 10^{-3}$. This leads to the conclusion that in $CP$-parity violation in the system of $K^o$ mesons there is no oscillation take place.

This was is devoted to the consideration of possible schemas of introduction of $CP$ violation for neutral mesons and quarks in weak interactions. It is noted that in general case it is incorrect to introduce $CP$ phase for first and third families only. These phases should be entered for all families and besides it is not mandatory these phases to be the same for all families. Besides this there are also considered the violations of $CP$ invariance for $K^o$, $D^o$, $B^o_d$, $B^o_s$ mesons, where except $CP$ phases also appear the mixing angles $\beta_1'$, $\beta_c$, $\beta_d$, $\beta_s$. We obtained the expressions for the probabilities of transitions in $CP$ violation for these mesons. In conclusion we discuss the schema of $CP$ violation for $d$, $s$, $b$ quarks, where appears their mixing angles and phases.

The anomalous magnetic moment of leptons is one of the best measured quantity in the physics of elementary particles. The difference of experimental value (E821-BNL) from theoretical prediction is of the level of 3-4 standard deviations.

Within non-local quark model the contribution from the process of light-by-light scattering is $a_{\mu}^{LbL} = 16.8 (1.25) \cdot 10^{-10}$.

The necessity for consideration of relativistic corrections to processes of pair charmonium production was explicitly demonstrated on the example of $e^+e^- \to J/\psi + \eta_c$ process, which cross section was measured by Belle and BaBar collaborations in 2002--2005. The first experimental results appeared to be in serious disagreement with earlier theoretical predictions, carried out in leading order of strong coupling constant $\alpha_s$ as well as of heavy quark velocity $v$ in the framework of nonrelativistic quantum chromodynamics (NRQCD) approach. The consequential calculation of several sorts of corrections, including an account of relativistic effects, caused by the relative motion of constituent quarks and antiquarks in meson, has finally reduced the discrepancy.

In the following talk, the calculation of relativistic corrections to the several processes of pair heavy hadrons production is presented. The described processes are interesting in relation with the existing or prospective experiments of high energy physics. In particular, the pair charmonium and double-heavy baryon production is studied.

On the basis of perturbative QCD and relativistic quark model, several types of corrections are considered. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving mesons are taken into account. For the gluon and quark propagators entering the amplitude, a truncated expansion in relative quark momenta is used. Relativistic corrections to the quark bound state wave functions are considered by means of the Breit-like potential. Comparison of the obtained results with existing experimental data and calculations within other approaches is discussed.

Within quantum chromodynamical $k_t$-factorization approach we calculated total and differential cross sections of inclusive and associative (with jets, includng jets from heavy quarks) production of direct photons in hadronic collisions and of photoproduction in electron-proton collisions and also production of lepton pairs in hadronic collisions at the energies of modern colliders. Our predictions are compared with different experimental data of D0, CDF, ATLAS, CMS, H1 and ZEUS collaborations.

In this work we studied the influence of large anomalous chromoagnetic moment of the quark (LACM) which is induced by non-perturbative structure of QCD vacuum in some reactionsat high energies. The existence of LACM effectivelly manifests in additional non-perturbative quark-gluon vertex. The main property of this vertex is the quark spin flip thus its contribution is important for spin-dependent observables.

We discuss the non-perturbative mechanism of transverse single-spin asymmetry in inclusive production of hadrons in $p p$ collisions which is based on the existence of LACM. This mechanism allows to explain large observable asymmetries at large transverse momenta.

We also evaluate the contributions of non-perturbative quark-gluon chromomagnetic interaction in the cross section of elastic $р р$ scattering at large momentum transfer. We show that odderon contribution into the cross section directly related with non-perturbative spin-flip vertex.

We consider exlusive electroproduction of $\rho$-meson of the proton $\gamma^* + p \to \rho^0 + p$. We show that LACM gives additional contribution into the cross section at small $Q^2$ in longitudional and in transverse polarization of virtual photon.

We derive light-cone sum rules for the electromagnetic nucleon form factors including the next-to-leading-order corrections for the contribution of twist-three and twist-four operators and a consistent treatment of the nucleon mass corrections. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations. A selfconsistent picture emerges, with the three valence quarks carrying $40\%:30\%:30\%$ of the proton momentum.

The first radial excitations of the $a_1$ and $f_1$ mesons are considered in the framework of the extended $U(2)\times U(2)$ Nambu--Jona-Lasinio model. For description of radially excited states we used the form factors of polynomial type of the second order over transverse quark momentum. Widths of a number of strong and radiative decays involving axial-vector mesons in the ground and the first radially excited states are calculated. We have got satisfactory agreement with experimental data for the ground states. A set of predictions for the excited states of mesons is given.

The necessity for consideration of relativistic corrections to processes of pair charmonium production was explicitly demonstrated on the example of $e^+e^- \to J/\psi + \eta_c$ process, which cross section was measured by Belle and BaBar collaborations in 2002--2005. The first experimental results appeared to be in serious disagreement with earlier theoretical predictions, carried out in leading order of strong coupling constant $\alpha_s$ as well as of heavy quark velocity $v$ in the framework of nonrelativistic quantum chromodynamics (NRQCD) approach. The consequential calculation of several sorts of corrections, including an account of relativistic effects, caused by the relative motion of constituent quarks and antiquarks in meson, has finally reduced the discrepancy.

In the following talk, the calculation of relativistic corrections to the processes of pair $S$-wave charmonium production in proton-proton interaction is presented. On the basis of perturbative QCD and relativistic quark model, several types of corrections are considered. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving mesons are taken into account. For the gluon and quark propagators entering the amplitude, a truncated expansion in relative quark momenta is used. Relativistic corrections to the quark bound state wave functions are considered by means of the Breit-like potential. The numerical results for cross sections are obtained at the LHC relative energies $\sqrt S = 7$ and 14 TeV. Comparison of the obtained results with existing experimental data and calculations within other approaches is discussed.

In the framework of the usual quantum electrodynamic (QED) the relativistic three dimensional (3D) Lippmann-Schwinger-type equations

$$ A_{e'p',ep}=V_{e'p',ep}+\sum_{e''p''}V_{e'p',e''p''}G_oA_{e''p'',ep} $$

for the $ep$ scattering amplitude $A_{e'p',ep}$, $ep$ scattering potential $V_{e'p',ep}$ and the free Green function $G_o$ are obtained. The $ep$ scattering potential $V_{e'p',ep}$ consists of the leading one off mass shell photon exchange part $V_{OPE}$ and the nonlocal potential $V_{NL}$ which contains all other possible contributions. Unlike to the other field-theoretical equations, both protons in $V_{e'p',ep}$ are on mass shell. Therefore in the suggested approach are not required the multi-variable input photon-nucleon vertexes with the off mass shell nucleons. It is demonstrated, that the suggested 3D relativistic equation have the same form in the formulations with and without quark degrees of freedom.

In the present formulation the standard leading one photon exchange potential $V_{OPE}$ is generated by the canonical (equal-time) anticommutator between the electron source and the interacted electron fields which are sandwiched by the one nucleon asymptotic states. This anticommutator is calculated in the Coulomb and Lorentz gauges, where only the transverse parts of the photon fields are quantized. It is shown, that the leading one photon exchange potential $V_{OPE}$ in the Coulomb and Lorentz gauges coincide. The complete set of the next-to leading order terms which are generated by the static electric (Coulomb) interaction and the nonlocal particle exchange potential $V_{NL}$ are exactly reproduced and analyzed.

The short review of the present theoretical and experimental status of the elastic $ep$ scattering up to 3-5 GeV energy region is given.