# The classical point electron in Colombeau’s theory of nonlinear generalized functions

@article{Gsponer2008TheCP, title={The classical point electron in Colombeau’s theory of nonlinear generalized functions}, author={Andr{\'e} Gsponer}, journal={Journal of Mathematical Physics}, year={2008}, volume={49}, pages={102901} }

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…

## 11 Citations

### The classical point-electron in the sequence algebra (C^infinity)^I

- Physics
- 2008

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…

### 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

- Physics
- 2008

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…

### A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics

- Physics, Mathematics
- 2006

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…

### 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

- Physics
- 2008

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…

### Study of the relativistic dynamics of extreme-mass-ratio inspirals

- Physics
- 2019

The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime - that is, where one mass is significantly smaller than the other - in the full context of…

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

- Mathematics
- 2008

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…

### Boundary conditions and generalized functions in a transition radiation problem

- Mathematics
- 2017

Abstract.The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of…

### A Paradox of Unity

- Mathematics
- 2018

In previous studies we found that generalized functions can be smooth, discrete, periodic or discrete periodic and they can either be local or global and they are regular or generalized functions. We…

### A Possible fundamental explanation of electroweak unification

- Mathematics
- 2008

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,…

### A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

## References

SHOWING 1-10 OF 50 REFERENCES

### General relativistic approach to the poincaré compensating stresses for the classical point electron

- Physics
- 1962

SummarySolutions are obtained for the Poincaré compensating energy-stress tensor for the classical point electron. The tensor, denoted byCνμ, may be chosen to cancel not only the divergent…

### Classical electrodynamics as a distribution theory

- PhysicsMathematical Proceedings of the Cambridge Philosophical Society
- 1956

ABSTRACT In this paper a precise distribution-theoretic formalism for the description of point charges interacting through a classical electromagnetic field is given. The distribution solutions of…

### Structure of the energy tensor in the classical electrodynamics of point particles

- Physics
- 1978

Classical electromagnetic theory provides an energy tensor defined off the particles's world line. The definition is extended to a distribution valid ''everywhere.'' The extended definition is…

### A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics

- Physics, Mathematics
- 2006

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…

### Examples of Momentum Distributions in the Electromagnetic Field and in Matter

- Physics
- 1969

Momentum conservation and the validity of the center-of-mass law are examined for systems made up of electrostaticcharges and magnets, in terms of the requirements of special relativitytheory. The…

### Nonlinearity and self-interaction in physical field theories with singularities

- Mathematics
- 1998

We investigate rigorous mathematical modeling of nonlinear problems in physical field theories involving differential geometric objects with singularities. We intend to develop a framework allowing…

### Distributions in spherical coordinates with applications to classical electrodynamics

- Physics
- 2004

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…

### On the electromagnetic momentum of static charge and steady current distributions

- Physics, Mathematics
- 2007

Faraday's and Furry's formulae for the electromagnetic momentum of static charge distributions combined with steady electric current distributions are generalized in order to obtain full agreement…

### Geodesics and geodesic deviation for impulsive gravitational waves

- Mathematics
- 1998

The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally…

### g=2 as the natural value of the tree-level gyromagnetic ratio of elementary particles.

- PhysicsPhysical review. D, Particles and fields
- 1992

A natural'' electromagnetic coupling prescription is implemented at the Lagrangian level, different from the minimal one, and yields, for elementary particles of [ital arbitrary][minus][ital spin], a gyromagnetic ratio [ital g]=2 at the tree level.