On the infrared behavior of the gluon propagator

Within the framework of gluodynamics, the well-known truncated Schwinger-Dyson equation for the gluon propagator is considered. The general case of power infrared behavior with noninteger exponents is investigated. The technique of extracting nonleading terms of the nonlinear integral equation, defined only by the infrared behavior of the propagator, is developed. The characteristic equation for the exponent is obtained and the interval of its values –1 c 3 is studied. It is shown that the equation for the gluon propagator in question has no solutions for the noninteger and nonhalf-integer power infrared behavior.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 250–263, February, 1996.     

Total gluon propagator in light-cone gauge and the transversality problem of the polarization operator in the infrared region. II

A three-gluon vertex that depends on a gauge vectorn and is free of kinematic and spurion (np)^–1 singularities in the physical region is constructed. It is shown that in the case of integer power-law asymptotic behavior of the gluon propagator there is separation of the singular contributions of the single- and two-loop diagrams in the Dyson—Schwinger equation. Necessary conditions for realization ofp ^–4 asymptotic behavior are obtained, and it is shown that an important role in their fulfillment is played by the parts of the three-gluon vertex that depend on the gauge vector. A solution of these conditions is found; when they are fulfilled, they lead to infrared asymptotic behaviors of the complete Dyson—Schwinger equation and its single-loop approximation that are mutually compatible.Tbilisi State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 14–23, July, 1994.     

Singular perturbed problems in the zero mass case: asymptotic behavior of spikes

We discuss the asymptotic behavior of the least energy solution of a Dirichlet problem in the zero mass case. If Q is a uniformly positive potential having k isolated local minima, then we prove the existence of a positive multi-spike solutions having k peaks concentrating at each local minima of the potential.     

Some regularizations of the temporal gauge and propagator of the Yang-Mills field

The paper continues earlier work of Slavnov and the author. Propagators of the Yang—Mills field are found by means of the Faddeev—Popov transition from the Coulomb to the temporal gauge with the use of two types of regularization. A comparison with already known results is made. Further possibilities are discussed.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 408–417, March, 1993.     

Equation for the quark propagator in the infrared region and some properties of its solutions

Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 85, No. 1, pp. 54–63, October, 1990.     

On the asymptotic behavior of some algorithms

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis techniques as it is usually done in this context. A new explicit representation of periodic functions involved is obtained at the same time. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005