Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The theory of the double preparation: discerned and indiscerned
  particles   In this paper we propose a deterministic and realistic quantum mechanics
interpretation which may correspond to Louis de Broglie's "double solution
theory". Louis de Broglie considers two solutions to the Schr\"odinger
equation, a singular and physical wave u representing the particle (soliton
wave) and a regular wave representing probability (statistical wave). We return
to the idea of two solutions, but in the form of an interpretation of the wave
function based on two different preparations of the quantum system. We
demonstrate the necessity of this double interpretation when the particles are
subjected to a semi-classical field by studying the convergence of the
Schr\"odinger equation when the Planck constant tends to 0. For this
convergence, we reexamine not only the foundations of quantum mechanics but
also those of classical mechanics, and in particular two important paradox of
classical mechanics: the interpretation of the principle of least action and
the the Gibbs paradox. We find two very different convergences which depend on
the preparation of the quantum particles: particles called indiscerned
(prepared in the same way and whose initial density is regular, such as atomic
beams) and particles called discerned (whose density is singular, such as
coherent states). These results are based on the Minplus analysis, a new branch
of mathematics that we have developed following Maslov, and on the Minplus path
integral which is the analog in classical mechanics of the Feynman path
integral in quantum mechanics. The indiscerned (or discerned) quantum particles
converge to indiscerned (or discerned) classical particles and we deduce that
the de Broglie-Bohm pilot wave is the correct interpretation for the
indiscerned quantum particles (wave statistics) and the Schr\"odinger
interpretation is the correct interpretation for discerned quantum particles
(wave soliton). Finally, we show that this double interpretation can be
extended to the non semi-classical case.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg