WAVE OPERATORS IN MODELS OF QFT
 Definition of an nonunitary dressing operator has been proposed and an existence of renormalized
wave operators in models of QFT is given.
 Equivalence of this renormalized wave operator and the Faddeev renormalized wave operators for the Lee model is given.

EXACT SMATRIX FOR SINGORDON
 The exact Smatrix for massive particles in the SinGordon model has been constructed.

BACKGROUND FORMULATION FOR SMATRIX
 Generating functional of the elements of the S matrix has been proposed. It has been shown that
in the formalism gauge dependent counter
terms do not arise at all.

1/N EXPANSION AND RENORMALIZABILITY
 Quantum field theory theory for the essentially nonlinear chiral field,
nonrenormalizable in three dimensional space time in the usual perturbation expansion, is constructed within 1/N expansion.
 A modified soft mass renormalization scheme for 1/N expansion of
the three dimensional O(N)invariant chiral field in the high and
lowtemperature phases, as well as at the critical point, is constructed.
 Generalized quantum chirality identities for composite operators are derived.
 The universal critical behaviour of the Ncomponent chiral field in three dimensions (the Kadanoff conjecture, 1966) is proved.

LOOP APPROACH TO GAUGE THEORIES
 An equivalence of a gauge theory to the chiral theory on the path is show.
 The renormalization of fields on a contour (Wilson loops) is proved.
 A representation for parallel transport along a closed contour
in a principal fiber bundle with connection in the form of an ordered integral over
a surface spanned by this contour (nonabelian version of the stokes formula) is proposed
and proved.

N=4, D=4 SUPERGAUGE THEORY
 The theorem about reconstruction of a superconnection in the N = 3 superspace
formulation of the N = 4 SYM theory in terms of onshell physical fields in Minkowski
space is proved.
 A new supersymmetric gaugeinvariant model is proposed and it is shown that the hiddensymmetry
algebra for this model is the KacMoody algebra without a center.

KALUZA–KLEIN THEORIES AND EXTRATIMELIKES DIMENSIONS
 Topological criteria for a compact manifold in higherdimensional
Kaluza–Klein theories with extra compactified timelike variables which
prevent the appearance of massless ghosts in an effective
fourdimensional theory are found.

(SUPER) STRING FIELD THEORY.
 An exact analytic solutions in the modified cubic fermionic string field
theory with the GSO() sector is constructed. This solution is interpreted as the string tachyon field
solution since it contains the GSO() tachyon local field and
reproduces the correct value for the nonBPS Dbrane tension.

HIGH ENERGY SCATTERING IN QCD HIGH ENERGY SCATTERING IN QCD
 The Regge regime of QCD as a special regime of lattice gauge theory
on an asymmetric lattice has been studied. Dynamics in this regime is described
by an effective twodimensional model.

PLANCKIAN ENERGY SCATTERING
 Collisions of ultrarelativistic particles are considered as collisions of plane gravitational waves and
producing in collisions of two plane gravitational waves a spacetime region which is locally
isometric to an interior of black hole solution is interpreted as a black form formation.
 Black hole production in the collision of ultrarelativistic particles in the braneworld approach
has been considered and the geometrical crossection of the black hole production is presented.

LARGE N MATRIX MODELS
 On stable sector in supermembrane matrix model is constructed

QDEFORMATIONS AND NONCOMMUTATIVE FIELD THEORIES
 The master fields for the large N limit of matrix models and gauge theory are
constructed. The master fields satisfy to standard equations of relativistic field
theory but fields are quantized according to a new rule. To define the master
field we use the Yang–Feldman equation with a free field quantized in the Boltzmannian
Fock space.

DBRANES AND PBRANES
 An algebraic method for a general construction of intersecting pbrane
solutions in diverse spacetime dimensions is developed.
 Nonextremal intersecting pbrane solutions of gravity coupled with several antisymmetric
fields and dilatons in various spacetime dimensions are constructed.

STRINGY MODEL OF COSMOLOGICAL DARK ENERGY
 SFT inspired model of the cosmological dark energy has been proposed.
A characteristic feature of the model is a possibility to cross the w=–1 barrier.
