The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang-big crunch) at the quantum level. We show that a proper study of their model does not indicate the it prevents the occurrence of singularities at the quantum level, in fact the quantum probability of such event is larger than the classical one. Our numerical simulations based on the powerful variational sinc collocation method (VSCM) also show that the precision of the results of that paper is much lower than the 20 significant digits reported by the authors. and it is formally equivalent to the Schrödinger equation for a quartic anharmonic oscillator with a potential givenV e (a) = 36ka 2 − 12Λa 4 .

We present a calculation of second class (SC) effects in τ decays induced by QCD corrections to the weak vertex [Formula: see text]. We find that the induced SC form factors behave like (md − mu)/q2 (q the momentum transfer, and mq the q-quark mass), which give branching ratios of O(10−6) and O(10−8) for the scalar and pseudotensor SC decays, respectively.

The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasi-time τ given by a function of the coordinate along the propagation axis in a classical combination z0 − t 2 F/m, while the diffraction effects along transverse axes are due solely to m/ . The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultra cold neutrons, Bose-Einstein condensates and molecular beams are proposed.PACS numbers: 03.75. Be, 04.20.Cv, 37.25.+k I.

We consider the finite-action classical solutions of Euclidean topologically massive gauge theories in the presence of external sources. We study the Abelian case for general sources, as well as the general non-Abelian case for weak sources. We also investigate the solutions within the radial Ansatz, both with the usual source coupling and with coupling to gauge-invariant sources. We show that all these solutions correspond to saddle points of the action.

No abstract