Irina Aref'eva

Main results

WAVE OPERATORS IN MODELS OF QFT
  • Definition of an non-unitary 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 S-MATRIX FOR SIN-GORDON
  • The exact S-matrix for massive particles in the Sin-Gordon model has been constructed.
BACKGROUND FORMULATION FOR S-MATRIX
  • 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, non-renormalizable 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 low-temperature 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 N-component 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 (non-abelian 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 on-shell physical fields in Minkowski space is proved.
  • A new supersymmetric gauge-invariant model is proposed and it is shown that the hidden-symmetry algebra for this model is the Kac-Moody algebra without a center.
KALUZA–KLEIN THEORIES AND EXTRA-TIME-LIKES DIMENSIONS
  • Topological criteria for a compact manifold in higher-dimensional Kaluza–Klein theories with extra compactified time-like variables which prevent the appearance of massless ghosts in an effective four-dimensional 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 D-brane 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 two-dimensional 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 space-time 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 ultra-relativistic particles in the brane-world 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
Q-DEFORMATIONS AND NON-COMMUTATIVE 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.
D-BRANES AND P-BRANES
  • An algebraic method for a general construction of intersecting p-brane solutions in diverse space-time dimensions is developed.
  • Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time 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.