dorsal/arxiv
View SchemaAxiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment
| Authors | Tomislav Ivezic |
|---|---|
| Categories | |
| ArXiv ID | physics/0412167 |
| URL | https://arxiv.org/abs/physics/0412167 |
| DOI | 10.1007/s10702-005-7533-7 |
| Journal | Found. Phys. Lett. 18, 401 (2005) |
Abstract
In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer independent expressions for the stress-energy vector T(n)(1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.
{
"annotation_id": "ca444837-9851-4d1c-a482-bfdb2c145464",
"date_created": "2026-03-02T18:00:57.059000Z",
"date_modified": "2026-03-02T18:00:57.059000Z",
"file_hash": "0d7e8fa7ab4129ebdce899155a70d75cea16dfb6abd612cb64e409a004d25e80",
"private": false,
"record": {
"abstract": "In this paper we present an axiomatic, geometric, formulation of\nelectromagnetism with only one axiom: the field equation for the Faraday\nbivector field F. This formulation with F field is a self-contained, complete\nand consistent formulation that dispenses with either electric and magnetic\nfields or the electromagnetic potentials. All physical quantities are defined\nwithout reference frames, the absolute quantities, i.e., they are geometric\nfour dimensional (4D) quantities or, when some basis is introduced, every\nquantity is represented as a 4D coordinate-based geometric quantity comprising\nboth components and a basis. The new observer independent expressions for the\nstress-energy vector T(n)(1-vector), the energy density U (scalar), the\nPoynting vector S and the momentum density g (1-vectors), the angular momentum\ndensity M (bivector) and the Lorentz force K (1-vector) are directly derived\nfrom the field equation for F. The local conservation laws are also directly\nderived from that field equation. The 1-vector Lagrangian with the F field as a\n4D absolute quantity is presented; the interaction term is written in terms of\nF and not, as usual, in terms of A. It is shown that this geometric formulation\nis in a full agreement with the Trouton-Noble experiment.",
"arxiv_id": "physics/0412167",
"authors": [
"Tomislav Ivezic"
],
"categories": [
"physics.gen-ph"
],
"doi": "10.1007/s10702-005-7533-7",
"journal_ref": "Found. Phys. Lett. 18, 401 (2005)",
"title": "Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment",
"url": "https://arxiv.org/abs/physics/0412167"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "17685bed-99af-4700-beb9-16301ed5ce58",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}