Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential families, Kahler geometry and quantum mechanics   Exponential families are a particular class of statistical manifolds which
are particularly important in statistical inference, and which appear very
frequently in statistics. For example, the set of normal distributions, with
mean {\mu} and deviation {\sigma}, form a 2-dimensional exponential family.
  In this paper, we show that the tangent bundle of an exponential family is
naturally a Kahler manifold. This simple but crucial observation leads to the
formalism of quantum mechanics in its geometrical form, i.e. based on the
Kahler structure of the complex projective space, but generalizes also to more
general Kahler manifolds, providing a natural geometric framework for the
description of quantum systems. Many questions related to this "statistical
Kahler geometry" are discussed, and a close connection with representation
theory is observed. Examples of physical relevance are treated in details. For
example, it is shown that the spin of a particle can be entirely understood by
means of the usual binomial distribution. This paper centers on the
mathematical foundations of quantum mechanics, and on the question of its
potential generalization through its geometrical formulation.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol