NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

ON THE MINIMUM ABSOLUTE VALUE of THE DISCRIMINANT of ABELIAN FIELDS of DEGREE p(2)

Let p be a prime number. A formula for the minimum absolute value of the discriminant of all Abelian extensions of Q of degree p(2) is given in terms of p.

EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Indirect constraints on the triple gauge boson couplings from Z -> b(b)over-bar partial width: An update

We update the indirect bounds on anomalous triple gauge couplings coming from the non-universal one-loop contributions to the Z --> width. These bounds, which are independent of the Higgs boson mass, are in agreement with the standard model predictions for the gauge boson self-couplings since the present value of R-b agrees fairly well with the theoretical estimates. Moreover, these indirect constraints on Delta g(1)(Z) and g(5)(Z) are most stringent than the present direct bounds on these quantities, while the indirect limit on lambda(Z) is weaker than the available experimental data.

Atomic radiative transitions in thermo field dynamics

In this work we rederive the Lamb-Retherford energy shift for an atomic electron in the presence of a thermal radiation. Using the Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) formalism, where physical observables are expressed as convolutions of suitable statistical functions, we construct the electromagnetic field propagator of thermo field dynamics in the Coulomb gauge in order to investigate finite temperature effects on the atomic energy levels. In the same context, we also analyze the problem of the ground state stability.

Bounds on direct couplings of superheavy metastable particles to the inflaton field from ultra high energy cosmic ray events

Top-down models for the origin of ultra high energy cosmic rays (UHECR's) propose that these events are the decay products of relic superheavy metastable particles, usually called X particles. These particles can be produced in the reheating period following the inflationary epoch of the early Universe. We obtain constraints on some parameters such as the lifetime and direct couplings of the X-particle to the inflaton field from the requirement that they are responsible for the observed UHECR flux.

Torsion and gravitation: A new view

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed.

First-order actions: A new view

We analyse systems described by first-order actions using the Hamilton-Jacobi (HJ) formalism for singular systems. In this study we verify that generalized brackets appear in a natural way in HJ approach, showing us the existence of a symplectic structure in the phase space of this formalism.

Scaling in few-body nuclear physics

The nuclear matter calculations with realistic nucleon-nucleon potentials present a general scaling between the nucleon-nucleus binding energy, the corresponding saturation density, and the triton binding energy. The Thomas-Efimov three-body effect implies in correlations among low-energy few-body and many-body observables. It is also well known that, by varying the short-range repulsion, keeping the two-nucleon information (deuteron and scattering) fixed, the four-nucleon and three-nucleon binding energies lie on a very narrow band known as a Tjon line. By looking for a universal scaling function connecting the proper scales of the few-body system with those of the many-body system, we suggest that the general nucleus-nucleon scaling mechanism is a manifestation of a universal few-body effect.

The quadratic spinor Lagrangian, axial torsion current and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field-Weyl, Majorana, flagpole, or flag-dipole spinor fields-yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

Large magnetic dipole moments for neutrinos with arbitrary non-calculable masses

We show that there is a general sort of neutrino effective interactions which allows, under certain conditions, to have relatively large magnetic dipole moments for neutrinos while keeping their masses non-calculable and arbitrarily small. The main ingredient of our mechanism for generating large magnetic moment to the neutrinos is the existence of a neutral scalar which has the only role to give mass to the neutrinos or the existence of flavor changing neutral currents in the neutrino sector. Although our approach is model independent, some models in which those interactions arise are commented.

Exact renormalization of massless QED(2)

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.

A dynamical mechanism to explain the top-bottom quark mass hierarchy

We discuss the mass splitting between the the top and bottom quarks in a technicolor scenario. The model proposed here contains a left-right electroweak gauge group. An extended technicolor group and mirror fermions are introduced. The top-bottom quark mass splitting turns out to be intimately connected to the breaking of the left-right gauge symmetry. Weak isospin violation occurs within the experimental limits.

Thermodynamics of quasi-particles

We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems with a temperature dependent Hamiltonian. We show that there are, in principle, an infinite number of solutions.