Abstract:
We suggest another approach to five-dimensional non-isotropic gauge theory. Using non-perturbative technique we show that already modest interaction anisotropy confines heavy bound states to four-dimensional layers, while free quarks propagate with almost no penalty into the fifth dimension.

Abstract:
We present our results on the non-perturbative evaluation of the renormalization constant for the quark field, $Z_q$, in Landau gauge within RI-MOM scheme. Using three lattice spacing we are able to isolate lattice artefacts of various origin, both perturbative and non-perturbative. In particular, the existence of the dimension-two gluon-condensate is discussed, and confirmed.

Abstract:
We calculate the free energy of a static quark anti-quark pair and the renormalized Polyakov loop in 2+1- and 3- flavor QCD using $16^3 \times 4$ and $16^3 \times 6$ lattices and improved staggered p4 action. We also compare the renormalized Polyakov loop with the results of our earlier studies.

Abstract:
Fermion determinant is computed analytically on extremely large lattices $% N_\tau \to \infty $ in the toy model approximation in which action is truncated so that in the Hamiltonian limit of $a_\tau \to 0$ all terms of order $a_\tau /a_\sigma $ are discarded$.$ Chiral condensate is studied in the area of small ($m<

Abstract:
Some consequences which follow from the periodicity assumption for spectral density of Wilson--Dirac operator are studied. Such an assumption allows to obtain simple representations for quark propagator, which reveals an important role of $m\leftrightarrow -m$ symmetry. It is argued that this symmetry is restored when the mirror fermion mass $m_r$ tended to infinity. The constrains on zero modes of Wilson--Dirac operator in a toy model approximation are also discussed.

Abstract:
We study the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using N_tau=4 and 6 lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.

Abstract:
odel for studying coupling dependence on lattice spacing a in gluodynamics is suggested. The model predicts $g-> g_{0}>0 with a->0. Free energy density in the model does not depend on temperature.

Abstract:
Transition from discrete to continuous Fourier series is studied for the functions becoming singular in the transition. Conditions are specified when summing replacement by integration is inadmissible.

Abstract:
Conditions when application of cyclization procedure does not lead to the periodic function are specified. Sufficient conditions under which obtained function is periodic are stated.