The Jacobi identity for Dirac-like brackets

For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order to illustrate our proof we work out explicitly the cases of a fractional spin particle in 2 + 1 dimensions and the original Brink-Schwarz massless superparticle in D = 10 dimensions in a Lorentz-covariant constraints separation.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Hamiltonian Formulation of the Yang-Mills field on the null-plane

We have studied the null plane hamiltonian structure of the free Yang Mills fields. Following the Dirac's procedure for constrained systems we have performed a detailed analysis of the constraint structure of the model and we give the generalized Dirac brackets for the physical variables. Using the correspondence principle in the Dime's brackets we obtain the same commutators present in the literature and new ones.

The canonical structure of Podolsky's generalized electrodynamics on the null-plane

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Two-dimensional induced gravity in reduced phase-space

We discuss the Dirac method analysis of two-dimensional induced gravity, coupled to bosonic matter fields, in reduced phase-space. After defining the extended Hamiltonian it is possible to fix the gauge completely. The Dirac brackets can all be obtained in closed form; nevertheless, the results are not particularly simple.

Symmetry transform in Faddeev-Jackiw quantization of dual models

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an electromagnetic potential described by a Chern-Simons term and second the Schwarz-Sen gauge theory, in order to obtain the complete set of non-null Dirac brackets and the correspondent Maxwell electromagnetic theory limit. ©1999 The American Physical Society.

Podolsky's electromagnetic theory on the null-plane gauge

Following the Dirac's technique for constrained systems we performed a detailed analysis of the constraint structure of Podolsky's electromagnetic theory on the null-plane coordinates. The null plane gauge condition was extended to second order theories and appropriate boundary conditions were imposed to guarantee the uniqueness of the inverse of the constraints matrix of the system. Finally, we determined the generalized Dirac brackets of the independent dynamical variables. © 2010 American Institute of Physics.

S Q E D (4) and Q E D (4) on the Null-Plane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect Of Composite Containing An Iodonium Salt On The Bond Strength Of Brackets To Bovine Enamel.

This study investigated the effect of the incorporation of an iodonium salt in experimental composites, on the bond strength of metallic brackets bonded to bovine teeth. Two hundred and seventy bovine teeth were embedded in self-curing acrylic resin and divided into 18 groups (n=15), according to the experimental composite with an iodonium salt at molar concentrations 0 (control), 0.5, or 1%; the light-activation times (8, 20 and 40 s); and the storage times (10 min or 24 h). Metallic brackets were fixed on the tooth surface using experimental composites. Photoactivation was performed with a quartz-tungsten-halogen light-curing unit curing unit for 8, 20 and 40 s. The specimens were stored in distilled water at 37 °C for 10 min or 24 h and submitted to bond strength test at 0.5 mm/min. The data were subjected to three-way ANOVA and Tukey's test (α=0.05). The Adhesive Remnant Index (ARI) was used to classify the failure modes. The shear bond strengths (MPa) at 10 min for light-activation times of 8, 20 and 40 s were: G1 - 4.6, 6.9 and 7.1; G2 - 8.1, 9.2 and 9.9; G3 - 9.1, 10.4 and 10.7; and at 24 h were: G1 - 10.9, 11.1 and 11.7; G2 - 11.8, 12.7 and 14.2; G3 - 12.1, 14.4 and 15.8. There was a predominance of ARI score 3 for groups with 10 min storage time, and ARI score 2 for groups with 24 h storage time. In conclusion, the addition of iodonium salt (C05 and C1) to the experimental composite may increase the bond strength of brackets to bovine enamel using reduced light exposure times.

Are torque values of preadjusted brackets precise?

OBJECTIVE: The aim of the present study was to verify the torque precision of metallic brackets with MBT prescription using the canine brackets as the representative sample of six commercial brands. MATERIAL AND METHODS: Twenty maxillary and 20 mandibular canine brackets of one of the following commercial brands were selected: 3M Unitek, Abzil, American Orthodontics, TP Orthodontics, Morelli and Ortho Organizers. The torque angle, established by reference points and lines, was measured by an operator using an optical microscope coupled to a computer. The values were compared to those established by the MBT prescription. RESULTS: The results showed that for the maxillary canine brackets, only the Morelli torque (-3.33º) presented statistically significant difference from the proposed values (-7º). For the mandibular canines, American Orthodontics (-6.34º) and Ortho Organizers (-6.25º) presented statistically significant differences from the standards (-6º). Comparing the brands, Morelli presented statistically significant differences in comparison with all the other brands for maxillary canine brackets. For the mandibular canine brackets, there was no statistically significant difference between the brands. CONCLUSIONS: There are significant variations in torque values of some of the brackets assessed, which would clinically compromise the buccolingual positioning of the tooth at the end of orthodontic treatment.

An in vitro comparison of nickel and chromium release from brackets

This study aimed at comparing amounts of nickel (Ni) and chromium (Cr) released from brackets from different manufacturers in simulated oral environments. 280 brackets were equally divided into 7 groups according to manufacturer. 6 groups of brackets were stainless steel, and 1 group of brackets was made of a cobalt-chromium alloy with low Ni content (0.5%). International standard ISO 10271/2001 was applied to provide test methods. Each bracket was immersed in 0.5 ml of synthetic saliva (SS) or artificial plaque fluid (PF) over a period of 28 days at 37ºC. Solutions were replaced every 7 days, and were analyzed by spectrometry. The Kruskal-Wallis test was applied. Amounts of Ni release in SS (µg L-1 per week) varied between groups from "bellow detection limits" to 694, and from 49 to 5,948.5 in PF. The group of brackets made of cobalt-chromium alloy, with the least nickel content, did not release the least amounts of Ni. Amounts of Cr detected in SS and in PF (µg L-1 per week) were from 1 to 10.4 and from 50.5 to 8,225, respectively. It was therefore concluded that brackets from different manufacturers present different corrosion behavior. Further studies are necessary to determine clinical implications of the findings.

Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of the spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spatial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external electromagnetic field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, Delta x Delta y >= theta(2)/2, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with 2+1-dimensional fermions interacting with 3+1-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.