arXiv subjects
Publications and source records attributed to Vladimir K. Petrov.
Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and conditions under which this ambiguity does not arise are suggested.
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is considered.
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 $Ω^{\prime}$.
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.
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.
Coupling dependence on lattice spacing and size is estimated analytically at β-> \infty region where for a->0 the critical area is shifted in accordance with Callan-Symanzik relation. In considered approximation no trace of critical behavior is found in this area.
Fermion propagator is computed in a simple model on an extremely anisotropic lattice $ξ\gg1$. Fermion determinant is evaluated up to $ξ^{-4}$ order. Chiral condensate is estimated in mean field approximation.
Cooled down and diluted quark-gluon matter is considered. A possibility of condensation of multiquark clusters with zero N-alities is discussed.
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.