### Abstract

Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell-Born-Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton-Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell-Born-Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.

Original language | English (US) |
---|---|

Pages (from-to) | 1057-1122 |

Number of pages | 66 |

Journal | Journal of Statistical Physics |

Volume | 116 |

Issue number | 1-4 |

DOIs | |

State | Published - Aug 1 2004 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Hamilton-Jacobi law of motion
- Pauli principle
- determinism: Maxwell-Born-Infeld field equations
- electromagnetism: electromagnetic fields
- permutability: configuration space
- point charges
- spacetime: special and general relativity

### Cite this

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*Journal of Statistical Physics*, vol. 116, no. 1-4, pp. 1057-1122. https://doi.org/10.1023/B:JOSS.0000037250.72634.2a

**Electromagnetic field theory without divergence problems 1. The born legacy.** / Kiessling, Michael.

Research output: Contribution to journal › Review article

TY - JOUR

T1 - Electromagnetic field theory without divergence problems 1. The born legacy

AU - Kiessling, Michael

PY - 2004/8/1

Y1 - 2004/8/1

N2 - Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell-Born-Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton-Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell-Born-Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.

AB - Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell-Born-Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton-Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell-Born-Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.

KW - Hamilton-Jacobi law of motion

KW - Pauli principle

KW - determinism: Maxwell-Born-Infeld field equations

KW - electromagnetism: electromagnetic fields

KW - permutability: configuration space

KW - point charges

KW - spacetime: special and general relativity

UR - http://www.scopus.com/inward/record.url?scp=4344661816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344661816&partnerID=8YFLogxK

U2 - 10.1023/B:JOSS.0000037250.72634.2a

DO - 10.1023/B:JOSS.0000037250.72634.2a

M3 - Review article

VL - 116

SP - 1057

EP - 1122

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-4

ER -