Department for Mathematical Methods in Theoretical Physics
  • Explicit expressions for the sef-consistent renormalized vacuum averages of two-point chronologically ordered correlators of the tensor fermionic currents in the n-dimensional quantum field models with non-degenerate and degenerate fermion mass spectra are obtained.
    V. Kucheryavy
  • New hierarchies of integrable equations in partial derivatives coinciding with the integrable modification of the non-abelean Toda equations are constructed.
    T. Skrypnyk
  • The notion of the cross superautoduality in the field theory is introduced. The corresponding equations in terms of component fields and superfields are written.
    A. Pavlyuk
  • The mechanism and the rate of the increasing of local anistropy in the system of 4 partons, generating in the early stage of the nucleus-nucleus collisions, is investigated. The obtained results define the initial conditions for the problem of isotropisation and thermalisation of the quark-gluon plasma.
    A. Nazarenko
  • The analysis of the possibilty to apply the models of q-Bose gas and the model of q,p-Bose gas to the description of the spectra and correlations of the photons registrated in the relativistic heavy ion collisions experiments shows the real applicability of the mentioned models together with the recently investigated bosons like pions and kaons to the description of the pecularities of the spectrum and correlations of photons. The perspectives of the application of the systems of Tamm-Dankoff type q-oscillators and the corresponding model of q-Bose gas to the description of the spectrum and correlations of photons (pions, kaons) in the above mentioned experiments and in the quantum optics is outlined.
    A. Gavrilik
  • A new type of deformed canonical commutation relations generalizing known deformations of q-oscillator is constructed. A realization of these commutation relations in the Fock space and in a functional space (in particular, in the space of analytic functions) is built. The corresponding generalized Heisenberg-Weyl algebra is constructed. The existence of a Hopf structure on this algebra is proved. The symmetry of the spectrum of the constructed deformed oscillator is investigated.
    I. Burban
  • The eigenvalues and the spectrum of the quantum Hamiltonians of some quantum integrable spin systems are found by means of algebraic Bethe anzats.
    T. Skrypnyk