Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Background Independent Quantum Mechanics, Metric of Quantum States, and
  Gravity: A Comprehensive Perspective   This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.

21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio