dorsal/arxiv
View SchemaClassical electrodynamics of point charges
| Authors | Massimo Marino |
|---|---|
| Categories | |
| ArXiv ID | physics/0110047 |
| URL | https://arxiv.org/abs/physics/0110047 |
| DOI | 10.1006/aphy.2002.6299 |
| Journal | Annals Phys. 301 (2002) 85-127 |
Abstract
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality and the relativistic covariance of the theory, and with no need for mass renormalization. The procedure is first used to obtain a finite expression for the electromagnetic energy-momentum of the system. We show that the relativistic Lorentz-Dirac equation can be deduced from the conservation of this electromagnetic energy-momentum plus the usual mechanical term. Then we derive a finite lagrangian, which depends on the particle variables and on the actual electromagnetic potentials at a given time. From this lagrangian the equations of motion of both particles and fields can be derived via Hamilton's variational principle. The hamiltonian formulation of the theory can be obtained in a straightforward way. This leads to an interesting comparison between the resulting divergence-free expression of the hamiltonian functional and the standard renormalization rules for perturbative quantum electrodynamics.
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"abstract": "A simple mathematical procedure is introduced which allows redefining in an\nexact way divergent integrals and limits that appear in the basic equations of\nclassical electrodynamics with point charges. In this way all divergences are\nat once removed without affecting the locality and the relativistic covariance\nof the theory, and with no need for mass renormalization. The procedure is\nfirst used to obtain a finite expression for the electromagnetic\nenergy-momentum of the system. We show that the relativistic Lorentz-Dirac\nequation can be deduced from the conservation of this electromagnetic\nenergy-momentum plus the usual mechanical term. Then we derive a finite\nlagrangian, which depends on the particle variables and on the actual\nelectromagnetic potentials at a given time. From this lagrangian the equations\nof motion of both particles and fields can be derived via Hamilton\u0027s\nvariational principle. The hamiltonian formulation of the theory can be\nobtained in a straightforward way. This leads to an interesting comparison\nbetween the resulting divergence-free expression of the hamiltonian functional\nand the standard renormalization rules for perturbative quantum\nelectrodynamics.",
"arxiv_id": "physics/0110047",
"authors": [
"Massimo Marino"
],
"categories": [
"physics.class-ph",
"hep-th",
"math-ph",
"math.MP",
"physics.gen-ph"
],
"doi": "10.1006/aphy.2002.6299",
"journal_ref": "Annals Phys. 301 (2002) 85-127",
"title": "Classical electrodynamics of point charges",
"url": "https://arxiv.org/abs/physics/0110047"
},
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