Layer World: Living on a layer in 5D SU(3)

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

Egalitarian Improvement to Democracy: Quark renormalization constants in N_f=2 QCD

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.Comment: version 2, correcte

Some remarks on cyclization and periodicity

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

Random membrane model for lattice gluodynamics

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

Fermion propagator at finite temperatures on extremely anisotropic lattice

Fermion propagator is computed in a simple model on an extremely anisotropic lattice $\xi\gg1$. Fermion determinant is evaluated up to $\xi^{-4}$ order. Chiral condensate is estimated in mean field approximation.Comment: 6 page

Possible Consequences of Conjectural Periodicity of Spectrum of Lattice Dirac Operator

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.Comment: 17 pages, Latex2

Primordial function and ambiguity in its determination

We study the possibility to reconstruct the primordial function for some periodic function. The procedure includes an analytical continuation of a discrete function for Fourier coefficients computation, that introduces an ambiguity. To establish conditions under which no ambiguity appears, the modification of Carlson theorem is suggested. In a case when no subsidiary condition is imposed, ambiguity in the definition of primordial function does not go beyond the functions which belong to space $\Omega^{\prime}$

Asymptotic transition from Fourier series to integrals in LGT

It is shown that in asymptotic transition from Fourier series to integrals an error and ambiguity may arise. Ambiguity reduces to a possibility of addition of some distribution to the result. Properties of such distributions are studied and conditions are established under which ambiguity doesn't arise. Method for correction computation is suggested and conditions for correction turning to zero are specified

Analytical study of fermion determinant and chiral condensate behavior at finite temperatures in toy model approximation

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 ($m<<T$) quark masses

Spatial string tension in gluodynamics at finite temperature in a spherical model approximation

Spatial string tension is computed in finite temperature gluodynamics on asymmetric lattices in a spherical model approximation. Conditions of scaling behavior are specified. Discrepancies with a standard renormalisation procedure are discussed.Comment: 13 pages, revte