184 research outputs found
First quantized electron and photon model of QED and radiative processes
In this study we combine the classical models of the massive and massless
spinning particles, derive the current-current interaction Lagrangian of the
particles from the gauge transformations of the classical spinors, and discuss
radiative processes in electrodynamics by using the solutions of the Dirac
equation and the quantum wave equations of the photon. The longitudinal
polarized photon states give a new idea about the vacuum concept in
electrodynamics.Comment: LaTeX file, 20 pages, 7 figures. to appear in Canadian Journal of
Physic
Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case
In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print
physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell
equations to exist, which propagate without distortion with Superluminal speed
along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those
solutions possessed therefore infinite energy. In this note we show how to
obtain, by contrast, finite-energy solutions, with the same localization and
Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az;
42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell equations;
Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy
waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves;
Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic
waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational
waves.]Comment: plain LaTeX file (12 pages), plus 10 figure
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry
(1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and
particle physics (from 1953 to 2006). We show how the consideration of
symmetries, largely used in physics since the end of the 1920's, gave rise to a
new format of the periodic table in the 1970's. More specifically, this paper
is concerned with the application of the group SO(4,2)xSU(2) to the periodic
table of chemical elements. It is shown how the Madelung rule of the atomic
shell model can be used for setting up a periodic table that can be further
rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative
results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry
(special issue to commemorate the one hundredth anniversary of the death of
Mendeleev who died in 1907); version 2: 16 pages; some sentences added;
acknowledgment and references added; misprints correcte
Potential Scattering in Dirac Field Theory
We develop the potential scattering of a spinor within the context of
perturbation field theory. As an application, we reproduce, up to second order
in the potential, the diffusion results for a potential barrier of quantum
mechanics. An immediate consequence is a simple generalization to arbitrary
potential forms, a feature not possible in quantum mechanics.Comment: 7 page
Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem
Consider a finite dimensional complex Hilbert space \cH, with dim(\cH)
\geq 3, define \bS(\cH):= \{x\in \cH \:|\: ||x||=1\}, and let \nu_\cH be
the unique regular Borel positive measure invariant under the action of the
unitary operators in \cH, with \nu_\cH(\bS(\cH))=1. We prove that if a
complex frame function f : \bS(\cH)\to \bC satisfies f \in \cL^2(\bS(\cH),
\nu_\cH), then it verifies Gleason's statement: There is a unique linear
operator A: \cH \to \cH such that for every u \in
\bS(\cH). is Hermitean when is real. No boundedness requirement is
thus assumed on {\em a priori}.Comment: 9 pages, Accepted for publication in Ann. H. Poincar\'
Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach
We investigate variations of the Zitterbewegung frequency of electron due to
an external static and uniform magnetic field employing the expectation value
quantum approach, and compare our results with the classical model of spinning
particles. We demonstrate that these two so far compatible approaches are not
in agreement in the presence of an external uniform static magnetic field, in
which the classical approach breaks the usual symmetry of free particles and
antiparticles states, i.e. it leads to CP violation. Hence, regarding the
Zitterbewegung frequency of electron, the classical approach in the presence of
an external magnetic field is unlikely to correctly describe the spin of
electron, while the quantum approach does, as expected. We also show that the
results obtained via the expectation value are in close agreement with the
quantum approach of the Heisenberg picture derived in the literature. However,
the method we use is capable of being compared with the classical approach
regarding the spin aspects. The classical interpretation of spin produced by
the altered Zitterbewegung frequency, in the presence of an external magnetic
field, are discussed.Comment: 16 pages, no figure
Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations
Pandres has developed a theory in which the geometrical structure of a real
four-dimensional space-time is expressed by a real orthonormal tetrad, and the
group of diffeomorphisms is replaced by a larger group called the conservation
group. This paper extends the geometrical foundation for Pandres' theory by
developing an appropriate covariant derivative which is covariant under all
local Lorentz (frame) transformations, including complex Lorentz
transformations, as well as conservative transformations. After defining this
extended covariant derivative, an appropriate Lagrangian and its resulting
field equations are derived. As in Pandres' theory, these field equations
result in a stress-energy tensor that has terms which may automatically
represent the electroweak field. Finally, the theory is extended to include
2-spinors and 4-spinors.Comment: Aug 25 replacement has corrected margin width
Shape Invariance and Its Connection to Potential Algebra
Exactly solvable potentials of nonrelativistic quantum mechanics are known to
be shape invariant. For these potentials, eigenvalues and eigenvectors can be
derived using well known methods of supersymmetric quantum mechanics. The
majority of these potentials have also been shown to possess a potential
algebra, and hence are also solvable by group theoretical techniques. In this
paper, for a subset of solvable problems, we establish a connection between the
two methods and show that they are indeed equivalent.Comment: Latex File, 10 pages, One figure available on request. Appeared in
the proceedings of the workshop on "Supersymmetric Quantum Mechanics and
Integrable Models" held at University of Illinois, June 12-14, 1997; Ed. H.
Aratyn et a
Path and Path Deviation Equations for p-branes
Path and path deviation equations for neutral, charged, spinning and spinning
charged test particles, using a modified Bazanski Lagrangian, are derived. We
extend this approach to strings and branes. We show how the Bazanski Lagrangian
for charged point particles and charged branes arises `a la Kaluza-Klein from
the Bazanski Lagrangian in 5-dimensions.Comment: 13 pages, LaTeX fil
Gazeau-Klauder type coherent states for hypergeometric type operators
The hypergeometric type operators are shape invariant, and a factorization
into a product of first order differential operators can be explicitly
described in the general case. Some additional shape invariant operators
depending on several parameters are defined in a natural way by starting from
this general factorization. The mathematical properties of the eigenfunctions
and eigenvalues of the operators thus obtained depend on the values of the
involved parameters. We study the parameter dependence of orthogonality, square
integrability and of the monotony of eigenvalue sequence. The obtained results
allow us to define certain systems of Gazeau-Klauder coherent states and to
describe some of their properties. Our systematic study recovers a number of
well-known results in a natural unified way and also leads to new findings.Comment: An error occurring in Theorem 12 and Theorem 13 has been correcte
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