Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The role of Dirac equations in the classical mechanics of the
  relativistic top   A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation
for a single particle with spin is presented. The general Hamilton-Jacobi
equation for the particle expressed in terms of a background Weyl's conformal
geometry is found to be linearized, exactly and in closed form, by an
\textit{ansatz} solution that can be straightforwardly interpreted as the
"quantum wave function" $\psi_4$ of the 4-spinor Dirac's equation. In
particular, all quantum features of the model arise from a subtle interplay
between the conformal curvature of the configuration space acting as a
potential and Weyl's "pre-potential" closely related to $\psi_4$, which acts on
the particle trajectory. The theory, carried out here by assuming a Minkowsky
metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the
one adopted in the context of General Relativity. This novel theoretical
scenario, referred to as "Affine Quantum Mechanics", appears to be of general
application and is expected to open a promising perspective in the modern
endeavor aimed at the unification of the natural forces with gravitation.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga