The Schr\" odinger picture of the Dirac quantum mechanics on spatially flat Robertson-Walker backgrounds

The Schr\" odinger picture of the Dirac quantum mechanics is defined in charts with spatially flat Robertson-Walker metrics and Cartesian coordinates. The main observables of this picture are identified, including the interacting part of the Hamiltonian operator produced by the minimal coupling with the gravitational field. It is shown that in this approach new Dirac quantum modes on de Sitter spacetimes may be found analytically solving the Dirac equation.Comment: 6 pages 0 figure

Lifetimes of Heavy-Flavour Hadrons -- Whence and Whither?

A theoretical treatment for the weak decays of heavy-flavour hadrons has been developed that is genuinely based on QCD. Its methodology as it applies to total lifetimes and the underlying theoretical issues are sketched. Predictions are compared with present data. One discrepancy emerges: the beauty baryon lifetime appears to be significantly shorter than expected. The ramifications of those findings are analyzed in detail.Comment: 15 pages, no figures, LATEX, two references added and new information concerning a lower charm content in B decays incorporate

Hidden 12-dimensional structures in AdS(5)xS(5) and M(4)xR(6) Supergravities

It is shown that AdS(5)xS(5) supergravity has hitherto unnoticed supersymmetric properties that are related to a hidden 12-dimensional structure. The totality of the AdS(5)xS(5) supergravity Kaluza-Klein towers is given by a single superfield that describes the quantum states of a 12-dimensional supersymmetric particle. The particle has super phase space (X,P,Theta) with (10,2) signature and 32 fermions. The worldline action is constructed as a generalization of the supersymmetric particle action in Two-Time Physics. SU(2,2|4) is a linearly realized global supersymmetry of the 2T action. The action is invariant under the gauge symmetries Sp(2,R), SO(4,2),SO(6), and fermionic kappa. These gauge symmetries insure unitarity and causality while allowing the reduction of the 12-dimensional super phase space to the correct super phase space for AdS(5)xS(5) or M(4)xR(6) with 16 fermions and one time, or other dually related one time spaces. One of the predictions of this formulation is that all of the SU(2,2|4) representations that describe Kaluza-Klein towers in AdS(5)xS(5) or M(4)xR(6) supergravity universally have vanishing eigenvalues for all the Casimir operators. This prediction has been verified directly in AdS(5)xS(5) supergravity. This suggests that the supergravity spectrum supports a hidden (10,2) structure. A possible duality between AdS(5)xS(5) and M(4)xR(6) supergravities is also indicated. Generalizations of the approach applicable 10-dimensional super Yang Mills theory and 11-dimensional M-theory are briefly discussed.Comment: LaTeX, 32 pages. v2 includes additional generalizations in the discussion section. The norm of J has been modified in eqs.(2.6, 3.3, 3.8). v3 includes a correction to Eq.(5.3

Geometric models of (d+1)-dimensional relativistic rotating oscillators

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.Comment: 7 pages, Late

Comparison Study in Using Plough, Tractor and Cultivator for Rice Field\u27 Land Preparation

Land preparation of the rice field is one of the most important steps for paddyplantation. Formerly plough is one of the main tools for land preparation, but now thefarmer used tractor or cultivator. From the farmer experience who are used that tools forland preparation there had advantages and disadvantages. The used of plough for landpreparation for long time ago the deep of rice field soil is constant because the ploughblade can be adjusted up and down. The plough can be turn to the right or left side so thatall part of rice field except the corner can be cultivate. But for pulling the plough must bedifficult to find two cows. While if using tractor or cultivator the right or left side and thecorner of the rice field can\u27t be cultivate. Deep of rice filed soil become shallow so thefertility of soil reduced. Beside that using tractor or cultivator for land preparation needmore fuel. The plough were easy to carry out, but tractor and cultivator difficult to carryout because the weight more that 200 kg

The leader operators of the (d+1)(d+1)-dimensional relativistic rotating oscillators

The main pairs of leader operators of the quantum models of relativistic rotating oscillators in arbitrary dimensions are derived. To this end one exploits the fact that these models generate P\"{o}schl-Teller radial problems with remarkable properties of supersymmetry and shape invariance.Comment: 11 page

CP, T and CPT Symmetries at the Turn of a New Millenium

After summarizing the status concerning CP violation in 1998 I describe the exciting developments of the last two years and extrapolate to the future. I comment on recent lessons about T and CPT invariance maninly from CPLEAR and emphasize the potential of finding New Physics by analyzing $K_{\mu 3}$ and charm decays and searching for electric dipole moments.Comment: 21 pages, LaTex, Lecture given at LEAP2000, Venice, Italy, Aug. 21 - 26, 200