Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maxwell's Equations, Hodge Theory, and Gravitation   A mathematical proof is given that Maxwell's equations are an {\it artifact}
of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms.
They are thus geometric in nature, independent of any specific physical
mechanisms, and valid for any force field -- attractive or repulsive --
generated by a material density and current. In particular, with appropriate
sign changes to reflect the attractive nature of the field, they apply to
gravitational fields on Minkowski space-time as well.
  The linearization of the Einstein Field Equations on Minkowksi space-time
leads also to a linear theory of gravity; but this theory is spin 2, while
Maxwell's field theory is spin 1. Hence the two theories are distinct. The
relationship of Maxwell's field theory to Einstein's geometric theory is
explained for weak fields.

2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
19
The categories of this paper are: eess