Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schr\"odinger Equation Describes a Particular Quantum Geometry   This paper posits the existence of, and finds a candidate for, a variable
change that allows quantum mechanics to be interpreted as quantum geometry. The
Bohr model of the Hydrogen atom is thought of in terms of an indeterministic
electron position and a deterministic metric and the motivation for this paper
is to try to change variables to have a deterministic position and momentum for
the electron and nucleus but with an indeterministic (quantum) metric that
reproduces the physics of the Bohr model. This mapping is achieved by allowing
the metric in the Hamiltonian to be different to the metric in the space-time
distance element and then representing the two metrics with vierbeins and
assuming they are canonically conjugate variables. Effectively, the usual
Schr\"odinger space-time variables have been re-interpreted as four of the
potentially sixteen parameters of the metric tensor vierbein in the distance
element while the metric tensor vierbein in the Hamiltonian is an operator
expressible as first-order derivatives in these variables or vice versa. I then
argue that this reproduces observed quantum physics at the sub-atomic level by
demonstrating the energy spectrum of electron orbitals is exactly the same as
the usual relativistic Bohr model for the Hydrogen atom in a certain limit.
Next, by introducing a single dimensionless running coupling that shows up in
the analogous place as, but in addition to, Planck's constant in the commutator
definition I argue that this allows massive objects to couple to the physical
space-time geometry but not massless ones - no matter coupling value. This
claim is based on a fit to the Schwarzschild metric with a few simple
assumptions and thus obtaining an effective theory of how the quantum
geometries at nearby space-time points couple to one another. This demonstrates
that this coupling constant is related to Newton's gravitational constant.

2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom