Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometrical hypotheses underlying wave functions and their
  emerging dynamics   Classical mechanics for individual physical systems and quantum mechanics of
non-relativistic particles are shown to be exceptional cases of a generalized
dynamics described in terms of maps between two manifolds, the source being
configuration space. The target space is argued to be 2-dimensional and flat,
and their orthogonal directions are physically interpreted. All terms in the
map equation have a geometrical meaning in the target space, and the pull-back
of its rotational Killing one-form allows the construction of a velocity field
in configuration space. Identification of this velocity field with tangent
vectors in the source space leads to the dynamical law of motion. For a
specific choice of an arbitrary scalar function present in the map equation,
and using Cartesian coordinates in the target space, the map equation becomes
linear and can be reduced to the Schr\"odinger equation. We link the
bi-dimensionality of the target space with the essential non-locality of
quantum mechanics. Many extensions of the framework here presented are
immediate, with deep consequences yet to be explored.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin