Higher Derivative Fermionic Field Equation in the First Order Formalism

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found which extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and non-minimal (anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first order equation has been obtained.Comment: 16 pages, title changed, new section, appendixes, and references adde

Klauder's coherent states for the radial Coulomb problem in a uniformly curved space and their flat-space limits

First a set of coherent states a la Klauder is formally constructed for the Coulomb problem in a curved space of constant curvature. Then the flat-space limit is taken to reduce the set for the radial Coulomb problem to a set of hydrogen atom coherent states corresponding to both the discrete and the continuous portions of the spectrum for a fixed \ell sector.Comment: 10 pages, no figure

Superluminal X-shaped beams propagating without distortion along a coaxial guide

In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.

Coherent states for the hydrogen atom

We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for the harmonic oscillator, with modifications due to the character of the problem.Comment: 6 pages, LATEX, using ioplppt.sty and iopfts.sty. v.2: some misprints are corrected. To appear in J.Phys.

Heat Kernel Asymptotics on Homogeneous Bundles

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.Comment: 29 pages, Proceedings of the 2007 Midwest Geometry Conference in Honor of Thomas P. Branso

Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

The EPRB experiment with massive partcles can be formulated if one defines spin in a relativistic way. Two versions are discussed: The one using the spin operator defined via the relativistic center-of-mass operator, and the one using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction for the EPRB experiment: The degree of violation of the Bell inequality DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The phenomenon can be physically understood as a combined effect of the Lorentz contraction and the Moller shift of the relativistic center of mass. The effect is therefore stronger than standard relativistic phenomena such as the Lorentz contraction or time dilatation. The fact that the Bell inequality is in general less violated than in the nonrelativistic case will have to be taken into account in tests for eavesdropping if massive particles will be used for a key transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important in the formula for eigenvector in Sec. IV); link to the unpublished 1984 paper containing the results (without typos!) of Sec. IV is adde

Conformal Symmetry and Duality between Free Particle, H-atom and Harmonic Oscillator

We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given as the lightcone momentum of an additional dimension. The duality is in the sense that the classical action of these systems are gauge fixed forms of the same worldline gauge theory action at the classical level, and they are all described by the same unitary representation of the conformal group SO(d,2) at the quantum level. The worldline action has a gauge symmetry Sp(2) which treats canonical variables (x,p) as doublets and exists only with a target spacetime that has d spacelike dimensions and two timelike dimensions. This spacetime is constrained due to the gauge symmetry, and the various dual solutions correspond to solutions of the constraints with different topologies. For example, for the H-atom the two timelike dimensions X^{0'},X^{0} live on a circle. The model provides an example of how realistic physics can be viewed as existing in a larger covariant space that includes two timelike coordinates, and how the covariance in the larger space unifies different looking physics into a single system.Comment: Latex, 23 pages, minor improvements. In v3 a better gauge choice for u for the H-atom is made; the results are the sam

Diamond degradation in hadron fields

The energy dependence of the concentration of primary displacements induced by protons and pions in diamond has been calculated in the energy range 50 MeV - 50 GeV, in the frame of the Lindhard theory. The concentrations of primary displacements induced by protons and pions have completely different energy dependencies: the proton degradation is very important at low energies, and is higher than the pion one in the whole energy range investigated, with the exception of the delta33 resonance region. Diamond has been found, theoretically, to be one order of magnitude more resistant to proton and pion irradiation in respect to silicon.Comment: 7 pages, 3 figure

Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.

Alternative Solution of the Path Integral for the Radial Coulomb Problem

In this Letter I present an alternative solution of the path integral for the radial Coulomb problem which is based on a two-dimensional singular version of the Levi-Civita transformation.Comment: 7 pages, Late