arXiv subjects

Andre Gsponer

Publications and source records attributed to Andre Gsponer.

At least 19 recordsLinked to original sources

arXiv2009

Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas

This report is a self-contained and comprehensive review of the physics of propagating pulses of high-intensity high-energy particle beams in pre-existing or self-generated plasmas. Consideration is given to beams of electrons, protons, muons, and their antiparticles, as well as to neutral-hydrogen, positronium, and electron-positron-plasmoid beams. The first part is a systematic overview of the theory pertaining to propagation, plasma self-generation, energy/current-losses, and stability of such pulses. The second part reviews the major full-scale propagation experiments which have been carried out, in atmospheric and outer-space plasmas, to assess the validity of theoretical models. It is found that the data available on these experiments demonstrate that range and stability are in agreement with theory. In particular, stable self-pinched propagation of high-current charged-particle beams in the atmosphere is possible over distances equal to several Nordsieck lengths. In order not to be deflected by Earth's magnetic field, electron-beam pulses need to be guided by a pre-formed channel, while proton-beam pulses may under suitable conditions propagate undeflected through both the low- and high-atmosphere. In ionospheric or outer-space plasmas, very-long-range propagation across Earth's magnetic field requires GeV to TeV electrons or positron beams in order for the transverse deflection to be acceptable, while undeflected propagation is possible for plasmoid beams consisting of co-moving high-energy particle pairs such as electrons and positrons.

physics.plasm-ph↗

arXiv2009

The physical heritage of Sir W.R. Hamilton

150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and quantum physics, and accepts carrying along the intricacies of the relativistic formalism. Examples are shown in classical dynamics, electrodynamics, and quantum theory. Lanczos's, Einstein's, and Petiau's generalizations of Dirac's equation are shown to be very naturally formulated with biquaternions. The discussion of spin, isospin, and mass quantization is greatly facilitated. Compared with other formalisms, biquaternions have the advantage of giving compact but at the same time explicit formulas which are directly usable for algebraic or numerical calculations.

math-ph↗

arXiv2008

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.

physics.class-ph↗

arXiv2008

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.

physics.class-ph↗

arXiv2008

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.

physics.class-ph↗

arXiv2008

Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. 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.

physics.class-ph↗

arXiv2008

A possible fundamental explanation of electroweak unification

Electroweak unification is implied by the local structure theorem of distribution theory applied to the causal interval R=X-Z between two space-time points X and Z. Taking R as generating function, the potentials of the electromagnetic and weak interactions are obtained by applying the causal d'Alembertian operator on R, and both potentials can be given a proper physical interpretation provided all calculations are made in the context of nonlinear generalized functions.

math-ph↗

arXiv2008

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.

math-ph↗

arXiv2008

The classical point-electron in Colombeau's theory of nonlinear generalized functions

The electric and magnetic fields of a pole-dipole singularity attributed to a point-electron-singularity in the Maxwell field are expressed in a Colombeau algebra of generalized functions. This enables one to calculate dynamical quantities quadratic in the fields which are otherwise mathematically ill-defined: The self-energy (i.e., `mass'), the self-angular momentum (i.e., `spin'), the self-momentum (i.e., `hidden momentum'), and the self-force. While the total self-force and self-momentum are zero, therefore insuring that the electron-singularity is stable, the mass and the spin are diverging integrals of delta-squared-functions. Yet, after renormalization according to standard prescriptions, the expressions for mass and spin are consistent with quantum theory, including the requirement of a gyromagnetic ratio greater than one. The most striking result, however, is that the electric and magnetic fields differ from the classical monopolar and dipolar fields by delta-function terms which are usually considered as insignificant, while in a Colombeau algebra these terms are precisely the sources of the mechanical mass and spin of the electron-singularity.

math-ph↗

arXiv2008

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.

gr-qc↗

arXiv2008

The origin of Iraq's nuclear weapons program: Technical reality and Western hypocrisy

This report is based on a series of papers written between 1980 and 2005 on the origin of Iraq's nuclear weapons program, which was known to one of the authors in the late 1970s already, as well as to a number of other physicists, who independently tried without success to inform their governments and the public. It is concluded that at no point did the Western governments effectively try to stop Iraq's nuclear weapons program, which suggests that its existence was useful as a foreign policy tool, as is confirmed by its use as a major justification to wage two wars on Iraq.

physics.soc-ph↗

arXiv2008

Lanczos's equation to replace Dirac's equation ?

Lanczos's quaternionic interpretation of Dirac's equation provides a unified description for all elementary particles of spin 0, 1/2, 1, and 3/2. The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero mass for the neutrino and the u-quark, are set by eigenvalue equations. The electro-weak interaction of the partons is the same as with the Standard model, with the same two free parameters: e and sin^2 theta. There is no need for a Higgs symmetry breaking mechanism. (2) Extended hadrons for which there is no simple eigenvalue equation for the mass. The strong interaction is essentially non-local. The pion mass and pion-nucleon coupling constant determine to first order the nucleon size, mass and anomalous magnetic moment.

hep-ph↗

arXiv2008

The sequence of ideas in a re-discovery of the Colombeau algebras

This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who prefer a `step-by-step approach' to a `top-down indoctrination.' No particular prerequisite knowledge is necessary -- and in less than one hour you should know everything you need to know and were afraid to ask about Colombeau algebras and their applications in physics... A selected bibliography is appended, giving examples of applications to partial differential and wave equations, electrodynamics, hydrodynamics, general relativity, and quantum field theory.

math-ph↗

arXiv2008

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.

math-ph↗

arXiv2008

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.

math-ph↗

arXiv2008

The Heisenberg-Pauli canonical formalism of quantum field theory in the rigorous setting of nonlinear generalized functions (Part I)

The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of generalized functions adapted to nonlinear operations. The free-field operators, their commutation relations, and the free-field Hamiltonian operator are calculated by a straightforward transcription of the usual formalism expressed in configuration space. This leads to the usual results, which are essentially independent of the regularization, with the exception of the zero-point energy which may be set to zero if a particular regularization is chosen. The calculations for the self-interacting field are more difficult, especially because of the well-known problems due to the unboundness of the operators and their time-dependent domains. Nevertheless, a proper methodology is developed and a differentiation on time-dependent domains is defined. The Heisenberg equations and the interacting-field equation are shown to be mathematically meaningful as operator-valued nonlinear generalized functions, which therefore provide an alternative to the usual Bogoliubov-Wightman interpretation of quantized fields as operator-valued distributions. The equation for the time-evolution operator is proved using two different methods, but no attempt is made to calculate the scattering operator, and the applications to perturbation theory are left to a subsequent report.

math-ph↗

arXiv2008

Quaternions in mathematical physics (1): Alphabetical bibliography

This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and identities. This quaternion bibliography will be further updated and corrected if necessary by the authors, who welcome any comment and reference that is not contained within the list.

math-ph↗

arXiv2008

Quaternions in mathematical physics (2): Analytical bibliography

This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and identities. This quaternion bibliography will be further updated and corrected if necessary by the authors, who welcome any comment and reference that is not contained within the list.

math-ph↗