[en] The significance of multiphonon structures as a basic excitation mode, covering the entire supersymmetric multiplet of U(6/4) is shown. (K.A.)

[en] The renormalization group invariant quark condensate μ is determinate both from the consistent equation for quark condensate in the chiral limit and from the Schwinger-Dyson (SD) equation improved by the intermediate range QCD force singular like δ (q) which is associated with the gluon condensate. The solutions of μ in these two equations are consistent. We also obtain the critical strong coupling constant αc above which chiral symmetry breaks in two approaches. The nonperturbative kernel of the SD equation makes αc smaller and μ bigger. An intuitive picture of the condensation above αc is discussed. In addition, with the help of the Slavnov-Taylor-Ward (STW) identity we derive the equations for the nonperturbative quark propagator from SD equation in the presence of the intermediate-range force is also responsible for dynamical chiral symmetry breaking. (author)

[en] Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang-Mills equations have. An Abelian two-parameter dual group is found to exist in gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real )solutions to the usual duality equations. Central symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein''s equations. However, the theory obtained reduces to the conformal-flat Nordstroem theory

[en] An original approach to constructing special type symmetries for boundary value problems, renormgroup symmetries, is reviewed. It is applied to a system of geometric optics equations. New solutions to the laser beam self-focusing problem are presented

[en] In supergravity models with low supersymmetry breaking scale the gravitinos can be superlight, with mass in the 10^-6 eV to few keV range. In such a case, gravitino emission provides a new cooling mechanism for protoneutron stars and therefore can provide constraints on the mass of a superlight gravitino. This happens because the coupling to matter of superlight gravitinos is dominated by its goldstino component, whose coupling to matter of superlight gravitinos is dominated by its goldstino component, whose coupling to matter is inversely proportional to the scale of supersymmetry breaking and increases as the gravitino mass decreases. Present observations therefore provide lower limits on the gravitino mass. Using the recently revised goldstino couplings, we find that the two dominant processes in supernova cooling are e⁺ e^- → GG and γ+e^- → e^- GG. They lead to a lower limit on the supersymmetry breaking scale Λ_s from 160 to 500 GeV for core temperatures 30 to 60 MeV and electron chemical potentials 200 to 300 MeV. The corresponding lower limits on the gravitino mass are .6 - 6 x 10^-6 eV

[en] Starting with two supersymmetric dual theories, we imagine adding a chiral perturbation that breaks supersymmetry dynamically. At low energy we then get two theories with soft supersymmetry-breaking terms that are generated dynamically. With a canonical Kaehler potential, some of the scalars of the ''magnetic'' theory typically have negative mass-squared, and the vector-like symmetry is broken. Since for large supersymmetry breaking the ''electric'' theory becomes ordinary QCD, the two theories are then incompatible. For small supersymmetry breaking, if duality still holds, the magnetic theory analysis implies specific patterns of chiral symmetry breaking in supersymmetric QCD with small soft masses

[en] Recently geometric duality was analyzed for a metric which admits Killing tensors. An interesting example arises when the manifold has Killing-Yano tensors. The symmetries of the dual metrics in the case of Taub-NUT metric are investigated. Generic and non-generic symmetries of dual Taub-NUT metric are analyzed

[en] The problem of chiral symmetry restoration at finite baryonic density and/or temperature is discussed. We first study the evolution of the quark condensate in nuclear mater and then address the question of the modification of the rho meson mass spectrum in connection with relativistic heavy ions collisions. (author)

[en] The structure of the algebra of the wave equations is studied. It is shown that the algebra of local symmetries of the massless wave equations is pertained to the Lee enveloping of the conformal group

[en] The relativistic exactly solvable one-dimensional models based on Askey-Wilson algebra as an algebra of dynamical symmetry are found. Some generalizations of the obtained results are discussed