A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics
| dc.creator | Gsponer, Andre | |
| dc.date | 2006-11-26 | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:19:15Z | |
| dc.date.available | 2026-07-07T10:19:15Z | |
| dc.description | 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. | |
| dc.description | 19 pages. Accepted for publication | |
| dc.identifier | https://arxiv.org/abs/math-ph/0611069 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0611069 | |
| dc.identifier | Eur. J. Phys. /30/ (2009) 109--126 | |
| dc.identifier | doi:10.1088/0143-0807/30/1/11 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174441 | |
| dc.subject | Mathematical Physics | |
| dc.title | A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics | |
| dc.type | text |