The Dirac equation without spinors

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac equation.Comment: 20 pages. Submitted for publication in the proceedings of the conference `Functional analysis, partial differential equations and applications', Rostock (Germany) 31 August--4 September 199

Aspects Of Heavy Quark Theory

Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i) basic parameters of the heavy quark theory; (ii) a class of exact QCD inequalities; (iii) new heavy quark sum rules; (iv) virial theorem; (v) applications (|V_cb| from the total semileptonic width and from the B->D* transition at zero recoil). In some instances new derivations of the previously known results are given, or new aspects addressed. In particular, we dwell on the exact QCD inequalities. Furthermore, a toy model is considered that may shed light on the controversy regarding the value of the kinetic energy of heavy quarks obtained by different methods.Comment: 67 pages, 6 Figures; plain LaTeX. Changes: Some equations in Sect.4 related to spin-nonsinglet sum rules are corrected. The references are updated

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

General entanglement

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.Comment: 7 pages, 1 figure,1 tabe, will be published in special issue of Journal of Physics (Conference Series) with Proceedings of CEWQO-200

Rotation and Spin in Physics

We delineate the role of rotation and spin in physics, discussing in order Newtonian classical physics, special relativity, quantum mechanics, quantum electrodynamics and general relativity. In the latter case, we discuss the generalization of the Kepler formula to post-Newtonian order $(c^{-2}$) including spin effects and two-body effects. Experiments which verify the theoretical results for general relativistic spin-orbit effects are discussed as well as efforts being made to verify the spin-spin effects

Heat transfer in solar absorber plates with micro-channels

Analytical, computational and experimental studies were carried out to investigate heat transfer and fluid flow in micro-channel absorber plates for compact (thin and light-weight) solar thermal collectors. The main objective of the work was to study different design and/or operating scenarios as well as study the significance of various micro-scaling effects. Analytical investigation showed that, under similar conditions, the proposed design yields a much higher fin efficiency, F and collector efficiency factor, F’ compared with the conventional solar collector design. An analytical model combining convective heat transfer in the collector fluid with axial conduction in the metal plate was developed. The predicted plate temperature profiles from the analytical model were in close agreement with the measured profiles. The model further showed that axial thermal conduction can significantly alter the plate temperature profile. Experiments were designed to represent real life operation of the proposed system. A CFD study, using the same design and operating parameters, produced results comparable with experiments. This numerical simulation also gave further insight into the heat transfer and fluid flow patterns in the micro-channel plate. The effect of channel cross section geometry was studied. The Nusselt number was observed to increase as the aspect ratio approached unity. Measured friction factors were similar in trend to the predictions for rectangular channels, although the overall rise in fluid temperature resulted in slightly lower friction factors. Thermal performance reduced slightly with increase in hydraulic diameter. The significance of various scaling effects was also investigated experimentally and numerically. Most of the typical scaling effects such as viscous dissipation and entrance effects were found to be insignificant however, conjugate heat transfer, surface boundary condition, surface finish and measurement uncertainties could be significant. The results showed a Reynolds number dependent Nusselt number which has been attributed to axial thermal conduction. It was also observed that only three walls were transferring heat; the walls of heat transfer had a uniform peripheral temperature while the heat flux varied peripherally. The closest simplified thermal boundary condition to represent heat transfer in these channels is the H1 with three (3) walls transferring heat. Increased surface roughness (obtained by using an etching technique to create the channels) was found to have a detrimental effect on heat transfer. The results showed that thermal improvement can be achieved by increasing the fluid velocity; however, pumping the thermal fluid above a pump power per plate area of 0.3 W/m2 resulted in marginal improvement. In practice, optimum microchannel geometry in plates should be sized based on fluid properties and operating conditions. The micro-channels should also have thin walls to minimise the effects of conjugate heat transfer. A Photovoltaic pump should be installed alongside the collector in order to provide pumping power required and minimise the overall fluid temperature rise. The results are beneficial for the design of micro-channel absorber plates for low heat flux operation up to 1000W/m2

Modeling electromagnetic form factors of light and heavy pseudoscalar mesons

The electromagnetic form factors of light and heavy pseudoscalar mesons are calculated within two covariant constituent-quark models, a light-front and a dispersion relation approach. We investigate the details and physical origins of the model dependence of various hadronic observables: the weak decay constant, the charge radius and the elastic electromagnetic form factor.Comment: 6 pages, 4 figures, use revtex4. Figure 2 and references are corrected. Acknoledgments are adde

Noninertial effects on a Dirac neutral particle inducing an analogue of the Landau quantization in the cosmic string spacetime

We discuss the behaviour of external fields that interact with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound states solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi-Walker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau-He-McKellar-Wilkens quantization in the cosmic string spacetime. Finally we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.Comment: 15 pages, no figure, this paper will be published in volume 42 of the Brazilian Journal of Physic