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

The self-interaction force on an arbitrarily moving point-charge and its energy-momentum radiation rate: A mathematically rigorous derivation of the Lorentz-Dirac equation of motion

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions and all calculations are made in a Colombeau algebra. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field. This solves, without changing anything in Maxwell's theory, numerous long-standing problems going back to more than a century. As an immediate application an unambiguous derivation of the Lorentz-Dirac equation of motion is given, and the origin of the problem with the Schott term is explained: it was due to the fact that the correct self-energy of a point charge is not the Coulomb self-energy, but an integral over a delta-squared function which yields a finite contribution to the Schott term that is either absent or incorrect in the customary formulations.Comment: 17 pages. Short version of arXiv:0812.481

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

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 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

What is spin?

This is a late answer to question #79 by R.I. Khrapko, "Does plane wave not carry a spin?," Am. J. Phys. /69/, 405 (2001), and a complement (on gauge invariance, massive spin 1 and 1/2, and massless spin 2 fields) to the paper by H.C. Ohanian, "What is spin?," Am. J. Phys. /54/, 500--505 (1985). In particular, it is confirmed that "spin" is a classical quantity which can be calculated for any field using its definition, namely that it is just the non-local part of the conserved angular momentum. This leads to explicit expressions which are bilinear in the fields and which agree with their standard "quantum" counterparts.Comment: Submitted to Am. J. Phys., 6 page