748 research outputs found
Derivation of the potential, field, and locally-conserved charge-current density of an arbitrarily moving point-charge
The complete charge-current density and field strength of an arbitrarily
accelerated relativistic point-charge are explicitly calculated. The current
density includes, apart from the well-established three-dimensional
delta-function which is sufficient for its global conservation, additional
delta-contributions depending on the second and third proper-time derivatives
of the position, which are necessary for its local conservation as required by
the internal consistency of classical electrodynamics which implies that local
charge-conservation is an {identity}. Similarly, the field strength includes an
additional delta-contribution which is necessary for obtaining this result. The
Lienard-Wiechert field and charge-current density must therefore be interpreted
as nonlinear generalized functions, i.e., not just as distributions, even
though only linear operations are necessary to verify charge-current
conservation. The four-potential from which this field and the conserved
charge-current density derive is found to be unique in the sense that it is the
only one reducing to an invariant scalar function in the instantaneous rest
frame of the point-charge that leads to a point-like locally-conserved
charge-current density.Comment: 25 pages. Long version of arXiv:physics/061209
A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics
The objective of this introduction to Colombeau algebras of
generalized-functions (in which distributions can be freely multiplied) is to
explain in elementary terms the essential concepts necessary for their
application to basic non-linear problems in classical physics.
Examples are given in hydrodynamics and electrodynamics. The problem of the
self-energy of a point electric charge is worked out in detail: The Coulomb
potential and field are defined as Colombeau generalized-functions, and
integrals of nonlinear expressions corresponding to products of distributions
(such as the square of the Coulomb field and the square of the delta-function)
are calculated.
Finally, the methods introduced in Eur. J. Phys. /28/ (2007) 267-275,
1021-1042, and 1241, to deal with point-like singularities in classical
electrodynamics are confirmed.Comment: 19 pages. Accepted for publicatio
Integer-quaternion formulation of Lambek's representation of fundamental particles and their interactions
Lambek's unified classification of the elementary interaction-quanta of the
``Standard model'' is formulated in terms of the 24 units of the
integer-quaternion ring, i.e., the tetrahedral group Q_{24}. An extension of
Lambek's scheme to the octahedral group Q_{48} may enable to take all three
generations of leptons and quarks into account, as well as to provide a
quantitative explanation for flavor-mixing.Comment: 10 pages, 3 tables. Error in the abstract correcte
Explicit closed-form parametrization of SU(3) and SU(4) in terms of complex quaternions and elementary functions
Remarkably simple closed-form expressions for the elements of the groups
SU(n), SL(n,R), and SL(n,C) with n=2, 3, and 4 are obtained using linear
functions of biquaternions instead of n x n matrices. These representations do
not directly generalize to SU(n>4). However, the quaternion methods used are
sufficiently general to find applications in quantum chromodynamics and other
problems which necessitate complicated 3 x 3 or 4 x 4 matrix calculations.Comment: Submitted to Journal of Mathematical Physics, 17 pages, 1 table
From the lab to the battlefield? Nanotechnology and fourth generation nuclear weapons
The paper addresses some major implications of microelectromechanical systems
(MEMS) engineering and nanotechnology for the improvement of existing types of
nuclear weapons, and the development of more robust versions of these weapons,
as well as for the development of fourth generations nuclear weapons in which
nanotechnology will play an essential role.Comment: 10 pages. Slightly expaned version with a few additional end-notes
and reference
On the physical interpretation of singularities in Lanczos-Newman electrodynamics
We discuss the physical nature of elementary singularities arising in the
complexified Maxwell field extended into complex spacetime, i.e., in
Lanczos-Newman electrodynamics, which may provide a possible link between
elementary particle physics and general relativity theory. We show that the
translation of the world-line of a bare (e.g., spinless) electric-monopole
singularity into imaginary space is adding a magnetic-dimonopole component to
it, so that it can be interpreted as a pseudoscalar pion-proton interaction
current, consistent which both charge-independent meson theory and zero-order
quantum chromodynamics. On the other hand, the interaction current of an
electric-monopole intrinsic-magnetic-dipole singularity characteristic of a
Dirac electron is obtained by another operation on the world-line, which
however does not seem to have a simple geometric interpretation. Nevertheless,
both operations can be given a covariant interpretation, which shows that the
corresponding interactions necessarily arise on an equal footing, and therefore
provides a connection between elementary particles and singularities in general
relativity.Comment: 22 pages. Final versio
The classical point-electron in the sequence algebra (C^infinity)^I
In arXiv:0806.4682 the self-energy and self-angular momentum (i.e.,
electromagnetic mass and spin) of a classical point-electron were calculated in
a Colombeau algebra. In the present paper these quantities are calculated in
the better known framework of `regularized distributions,' i.e., the customary
setting used in field-theory to manipulate diverging integrals, distributions,
and their products. The purpose is to compare these two frameworks, and to
highlight the reasons why the Colombeau theory of nonlinear generalized
functions could be the physically preferred setting for making these
calculations. In particular, it is shown that, in the Colombeau algebra, the
point-electron's mass and spin are {exact} integrals of squares of
delta-functions, whereas this is only an approximation in the customary
framework.Comment: 20 pages. Few minor corrections and updates of reference
First-order quantum perturbation theory and Colombeau generalized functions
The electromagnetic scattering of a spin-0 charged particle off a fixed
center is calculated in first-order quantum perturbation theory.
This implies evaluating the square of a `Dirac delta-function,' an operation
that is not defined in Schwartz distribution theory, and which in elementary
text-books is dealt with according to `Fermi's golden rule.'
In this paper these conventional calculations are carefully reviewed, and
their crucial parts reformulated in a Colombeau algebra -- in which the product
of distributions is mathematically well defined.
The conclusions are: (1) The Dirac delta-function insuring energy
conservation in first order perturbation theory belongs to a particular subset
of representatives of the Schwartz distribution defined by the Dirac measure.
These particular representatives have a well-defined square, and lead to a
physically meaningful result in agreement with the data. (2) A truly consistent
mathematical interpretation of these representatives is provided by their
redefinition as Colombeau generalized functions. This implies that their
square, and therefore the quantum mechanical rule leading from amplitudes to
probabilities, is rigorously defined.Comment: 16 page
The locally-conserved current density of the Lienard-Wiechert field
The complete charge-current density and field strength of an arbitrarily
accelerated relativistic point-charge are explicitly calculated. That current
includes, apart from the well-established delta-function term which is
sufficient for its global conservation, additional contributions depending on
the second and third proper-time derivatives of the position. These extra
contributions are necessary for the local conservation of that current, whose
divergence must vanish {identically} even if it is a distribution, as is the
case here. Similarly, the field strength includes an additional delta-like
contribution which is necessary for obtaining this result. Altogether, the
Lienard-Wiechert field and charge-current density must therefore be interpreted
as nonlinear generalized functions, i.e., not just as distributions, even
though only linear operations are needed to verify local charge-current
conservation.Comment: 9 pages. Short version of arXiv:physics/061223
Distributions in spherical coordinates with applications to classical electrodynamics
A general and rigorous method to deal with singularities at the origin of a
polar coordinate system is presented. Its power derives from a clear
distinction between the radial distance and the radial coordinate variable,
which makes that all delta-functions and their derivatives are automatically
generated, and insures that the Gauss theorem is correct for any distribution
with a finite number of isolated point-like singularities.
The method is applied to the Coulomb field, and to show the intrinsic
differences between the dipole and dimonopole fields in classical
electrodynamics.
In all cases the method directly leads to the general expressions required by
the internal consistency of classical electrodynamics.Comment: 12 pages. Final published version with a few typographical errors
correcte
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