Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the triatomic molecules 4He 3, 4He 2- 6Li, 4He 2- 7Li, and 4He 2- 23Na were calculated using a renormalized three-body model with a pairwise Dirac-δ interaction, having as physical inputs only the values of the binding energies of the diatomic and triatomic molecules. Molecular three-body systems with bound subsystems were considered. The resultant data were analyzed in detail.

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of s^l(n) (n = 2, 3) is presented explicitly. © SISSA/ISAS 2003.

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Efficacy of ultrasonic, electric and manual toothbrushes in patients with fixed orthodontic appliances

Objective: This crossover study compared the efficacy of an ultrasonic toothbrush for the reduction of plaque, gingival inflammation, and levels of Streptococcus mutans, in relation to an electric and a manual toothbrush. Materials and Methods: Twenty-one patients with orthodontic appliances were divided into three groups. All patients were evaluated by a periodontist and samples of saliva were collected for quantification of S mutans. The patients received their first brushes with appropriate instructions. For each crossover leg, patients used each toothbrush for a period of 30 days. At the end of each washout period, participants received a periodontal evaluation and new samples of saliva were collected. After 15 days of using their own toothbrushes, patients received the next toothbrushes in the experimental sequence. Results: The ultrasonic brush group presented significant improvement in the reduction of visible plaque on the buccal surfaces (-6.36%, P = .007). The counts of S mutans decreased in the electric (2.04 × 105 to 1.36 × 105 colony-forming units [CFU]/mL) and ultrasonic (2.98 × 105 to 1.84 × 105 CFU/mL) groups. There were no statistical differences among the three brushes for the clinical and microbiological parameters evaluated. Conclusions: This study did not demonstrate that the ultrasonic toothbrush was better in reducing gingival inflammation in adolescent orthodontic patients, but plaque scores were lowered on buccal surfaces of teeth with orthodontic brackets. In addition, S mutans counts were markedly decreased in the electric and ultrasonic groups, which should be related to a reduced risk of oral disease. © 2006 by The EH Angle Education and Research Foundation, Inc.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result. © 2007 The American Physical Society.

The Schwinger model on the null-plane

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory. © World Scientific Publishing Company.

Occurrence, extension, and severity of gingival margin alterations after orthodontic treatment.

To assess the occurrence, extension, and severity of gingival margin alterations in a sample of youth after orthodontic treatment. Records from 209 Caucasian adolescents (118 female and 91 male) before and after orthodontic treatment were selected. Patients presented a mean age at the beginning of orthodontic treatment of 11.20 ± 1.86 years and a final mean age of 14.72 ± 1.83 years. Class I and II patients with mandibular incisors and canines that were completely erupted and with spacing or crowding not exceeding 4 mm were evaluated. The presence of gingival recession on the labial surface of the mandibular anterior teeth was evaluated in intraoral photographs and casts made before and after treatment. The proportion of patients with gingival recession after treatment was statistically higher than at the beginning (P<.001). After orthodontic treatment, gingival recession was not present in any of the teeth for 63.6% of the patients; in 29.2% of the patients, recession was present in at least 1 tooth. In terms of severity, the majority of affected teeth (47%) presented gingival recession less than 2 mm and in 2% more than 4 mm. It may be concluded that alterations in the gingival margin, especially gingival recession, occur in patients after orthodontic therapy, but the extent and severity of this finding are low. COPYRIGHT © 2007 BY QUINTESSENCE PUBLISHING CO, INC.

Comparison of the shear bond strengths of conventional mesh bases and sandblasted orthodontic bracket bases

This study aimed to compare in vitro the shear bond strength between metallic brackets (Abzil) with conventional mesh bases and metallic brackets with bases industrially sandblasted with aluminum oxide using three adhesive systems, in order to assess the influence of sandblasting on adhesiveness and to compare 3 different bonding systems. Two hundred and forty bovine incisors were used and randomly divided into 6 groups (40 teeth in each group), according to the bracket base and to the bonding system. The brackets were direct-bonded in bovine teeth with 3 adhesive systems: System A - conventional Transbond™ XT (3M -Unitek); System B - Transbond™ Plus Self Etching Primer + Transbond™ XT (3M - Unitek) and System C - Fuji ORTHO LC resin-reinforced glass ionomer cement in capsules (GC Corp.). Shear bond strength tests were performed 24 hours after bonding, in a DL-3000 universal testing machine (EMIC), using a load cell of 200 kgf and a speed of 1 mm/min. The results were submitted to statistical analysis and showed no significant difference between conventional and sandblasted bracket bases. However, comparison between the bonding systems presented significantly different results. System A (14.92 MPa) and system C (13.24 MPa) presented statistically greater shear bond strength when compared to system B (10.66 MPa). There was no statistically significant difference between system A and system C.

Hamilton-Jacobi formalism on the null-plane: Applications

In this work we discuss the Hamilton-Jacobi formalism for fields on the null-plane. The Real Scalar Field in (1+1) - dimensions is studied since in it lays crucial points that are presented in more structured fields as the Electromagnetic case. The Hamilton-Jacobi formalism leads to the equations of motion for these systems after computing their respective Generalized Brackets. Copyright © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.