Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis as a source of geometry: a non-geometric representation of the
  Dirac equation   Consider a formally self-adjoint first order linear differential operator
acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold
without boundary. We examine the geometric content of such an operator and show
that it implicitly contains a Lorentzian metric, Pauli matrices, connection
coefficients for spinor fields and an electromagnetic covector potential. This
observation allows us to give a simple representation of the massive Dirac
equation as a system of four scalar equations involving an arbitrary two-by-two
matrix operator as above and its adjugate. The point of the paper is that in
order to write down the Dirac equation in the physically meaningful
4-dimensional hyperbolic setting one does not need any geometric constructs.
All the geometry required is contained in a single analytic object - an
abstract formally self-adjoint first order linear differential operator acting
on pairs of complex-valued scalar fields.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th