Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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   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.

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The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph