Gregory Vereshkov

QUANTUM GEOMETRODYNAMICS OF THE BIANCHI-IX MODEL IN EXTENDED PHASE SPACE

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the traditional Wheeler–DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrodinger equation. The Wheeler–DeWitt quantum geometrodynamics is represented a singular, BRST-invariant solution to the Schrodinger equation having no property of normalizability.

Radiative and Hadronic Decays of Vector Mesons in the Gauge Model of Quark-meson Interactions

Failing an exact nonperturbative theory, hadron interactions at low energies are considered in terms of effective Lagrangians, following both from fundamental theory (QCD) and dynamical symmetry concepts. The last approach allows to account for meson-meson and (constituent) quark-meson interactions combined with the VMD ideas in the generalized linear sigma-model (LσM) [1]. To formulate the gauge description of low-energy hadron phenomenology, we used the LσM inspired scheme with U0(1)×U(1)×SU(2) gauge symmetry. It is the simplest group to analyze (non-chiral) electromagnetic and strong mesonmeson and quark-meson interactions. Light vector mesons ρ, ω and photon arise in the model as gauge fields realizing tree level VMD and electromagnetic interaction due to extra U(1) groups. To consider the strong effects, SU(2) group, i.e. diagonal sum of SUL,R(2) subgroups of the global chiral group, is localized. After the spontaneous breaking of the U0(1) × U(1) × SU(2) local symmetry, residual scalar degrees of freedom (Higgs fields) can be associated with the scalar isotriplet a0(980) and singlet f0(980), and σmeson is interpreted as f0(600) state (for details see [2]). Their mass spectrum and decay properties are reasonably described due to free parameters in the scalar sector. In the model, vector fields couplings universality bounds in the gauge sector the number of free parameters (couplings, mixing angles), which are fixed by the data on two-particle decays (Γ(ρ → ππ), Γ(ω → ππ)) and masses of vector mesons [3]. Namely, we get g 0 /4π = 7.32 ·10, g 1 /4π = 2.86, g 2 /4π = 2.81, sinφ = 0.031, sin θ = 0.051. These values were used for the calculation of the vector meson decay widths to verify the gauge VMD approach in radiative decays ρ → ππγ and ω → ππγ at the tree level of meson-meson sector. The model quark-meson sector is tested in processes with quark loops: ρ → πγ, ω → πγ and ω(ρ) → πππ. Note, in calculations we use strong couplings as effective final values, without any loop corrections. But electromagnetic vertices are renormalized by the strong interactions. The differential width of ρ → ππγ can be presented in the form: