Dynamics of multidimensional generalization of Bianchi type-IX cosmological models.
We investigate the dynamics of an 11-dimensional homogeneous cosmological model. We assume that the t = const hypersurfaces are products of a 3-dimensional Bianchi type-IX space and a 7-dimensional torus. Most results of our investigation hold when the 7-dimensional torus is replaced by an m-dimensional torus T/sup m/. We show that for a large class of vacuum solutions the physical space expands while the microspace contracts providing a natural mechanism of dimensional reduction. Matter satisfying a simple barotropic equation of state always breaks the process of dynamical dimensional reduction. With special attention we study the behavior of our model close to the initial singularity. In contrast with the 4-dimensional Bianchi type-IX cosmological model the Kasner solution always describes an approach to the initial singularity. We study the transition from the Kasner regime to the oscillatory regime. We show that matter does not significantly change this property. We have found some exact solutions; they describe isotropic physical space, and axially symmetric physical space. We also investigate high-temperature quantum effects and their effects on the dynamics of our model. We show that the high-temperature quantum corrections do not depend on the geometrical properties of space, provided it is compact. The high-temperature quantummore » corrections can be described by a macroscopic equation of state satisfied by radiation.« less

title: Kantowski-Sachs multidimensional cosmological models and dynamical dimensional reduction
abstract: Einstein's field equations are solved for a multidimensional spacetime (KS)*Tm, where (KS) is a four-dimensional Kantowski-Sachs' spacetime (1966) and Tm is an m-dimensional torus. Among all possible vacuum solutions there is a large class of spacetimes in which the macroscopic space expands and the microscopic space contracts to a finite volume. The authors also consider a non-vacuum case and they explicitly solve the field equations for the matter satisfying the Zel'dovich equations of state (1987). In non-vacuum models, with matter satisfying an equation of state rho = gamma rho . O<or= gamma rho (1, at a sufficiently late stage of evolution the microspace always expands and the dynamical dimensional reduction does not occur. Models (KS)*B(IX)*S1*S1*S1*S1 and (KS)*B(IX)*B(IX)*S1, where B(IX) is the Bianchi type-IX space, are also briefly discussed. It is shown that there is no chaotic behaviour in these cases. The same conclusion is also valid when one-loop high-temperature quantum corrections generated by a massless scalar field are taken into account.

title: Generic and nongeneric world models
abstract: Catastrophe theory methods are employed to obtain a new classification of those world models which can be presented in the form of gradient dynamical systems. Generic sets and structural stability of models in the potential space are strictly defined. It is shown that if a cosmological model is required to be Friedman and generic, it must be flat.

title: On dynamical dimensional reduction
abstract: A mechanism is discussed of the dynamical dimensional reduction in the model B(I)×B(IX), where B(I) and B(IX) denote Bianchi I and Bianchi IX models respectively, in approximation of small anisotropies: the space with the isotropic internal sector is not reached monotonically, but exhibits oscillations around the isotropic state.

title: TOWARDS NONCOMMUTATIVE QUANTIZATION OF GRAVITY
abstract: We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity with those of quantum mechanics, and leads to correct “limiting cases” of both these physical theories. We (algebraically) quantize a groupoid constructed on space-time rather than space-time itself. Both space and time emerge in the transition process to the commutative case. Our approach clearly suggests that quantum gravitational observables should be looked for among correlations of distant phenomena rather than among local effects. A toy model is computed (based on a finite group) which predicts the value of “cosmological constants” (in the quantum sector) which vanish when going to the standard space-time physics.

title: Differential structure of space-time and its prolongations to singular boundaries
abstract: After briefly presenting basic ideas of the differential space theory, the global description of space-times in terms of this theory is given. The space-times of a straight cosmic string and that of the closed Friedman world model are our standard examples. A space-time with its singular boundary is no longer a differentiable manifold, but it can be organized into a differential space, and the differential structure of space-time can be prolonged to its singular boundary. In general, the procedure is not unique. A simple classification of differential structure prolongations is also presented.

title: Hadron thermodynamics with Wilson quarks.
abstract: We study hadron thermodynamics with Wilson quarks. The crossover curve between the high- and low-temperature phases is determined as a function of gauge coupling and hopping parameter on 8{sup 3}{times}4 lattices. Screening lengths are calculated in the vicinity of the crossover region, and meson masses are calculated along the crossover curve on 8{sup 2}{times}16{times}4 and 8{sup 3}{times}16 lattices, respectively.

title: Precise measurement of the Xi - magnetic moment.
abstract: With 4.36{times}10{sup 6} events, spin precession in a magnetic field has been used to measure the magnetic moment of the {Xi}{sup {minus}} hyperon as {minus}0.6505{plus minus}0.0025 nuclear magnetons.

title: Evidence for muon production by particles from Cygnus X-3.
abstract: We have observed underground cosmic-ray muons, corresponding to a secondary flux of  x 10/sup -11/ cm/sup -2/ s/sup -1/, at a depth of 1800-m water equivalent, which appear to be initiated by Cygnus X-3. This identification is based on both direction and phase coherence. The existence of such secondary muons conflicts with the current understanding of photon cascades and/or the nature and location of Cygnus X-3.

title: Thermodynamics of lattice QCD with two light quarks on a 16(3) x 8 lattice.
abstract: We have carried out a numerical study of the high-temperature behavior of lattice QCD with two flavors of staggered quarks. Our simulations were performed on 16 3 × 8 lattices with a quark mass m q = 0.0125, in units of the inverse lattice spacing. By monitoring the Wilson-Polyakov line, the chiral order parameter , and the average plaquette, we have determined that a crossover between the low-temperature state of ordinary hadronic matter and the high-temperature quark-gluon plasma occurs at a gauge coupling of 6/g 2 = 5. 54(2). Thermodynamic quantities do not show a large jump, although the equilibration time becomes quite long in the vicinity of the crossover. We have measured the entropy densities in the neighborhood of the crossover and further into the plasma phase

title: Effects of spatial size, lattice doubling, and source operators on the hadron spectrum with dynamical staggered quarks at 6/g2=5.6.
abstract: We have extended our previous study of the lattice QCD spectrum with two flavors of staggered dynamical quarks at 6/[ital g][sup 2]=5.6 and [ital am][sub [ital q]]=0.025 and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the [Delta] mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that [ital m][sub [pi]][sup 2][proportional to][ital m][sub [ital q]], and [ital f][sub [pi]] is estimated. Use of undoubled lattices removes the problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of [ital am][sub [ital q]]=0.01 when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, [ital am][sub [ital q]]=0.025. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.