Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On de Broglie's soliton wave function of many particles with finite
  masses, energies and momenta   We consider a mass-less manifestly covariant {\it linear} Schr\"odinger
equation. First, we show that it possesses a class of non-dispersive soliton
solution with finite-size spatio-temporal support inside which the quantum
amplitude satisfies the Klein-Gordon equation with finite {\it emergent} mass.
We then proceed to interpret the soliton wave function as describing a particle
with finite mass, energy and momentum. Inside the spatio-temporal support, the
wave function shows spatio-temporal internal vibration with angular frequency
and wave number that are determined by the energy-momentum of the particle as
firstly conjectured by de Broglie. Imposing resonance of the internal vibration
inside the spatio-temporal support leads to Planck-Einstein quantization of
energy-momentum. The first resonance mode is shown to recover the classical
energy-momentum relation developed in special relativity. We further show that
the linearity of the Schr\"odinger equation allows one to construct many
solitons solution through superposition, each describing a particle with
various masses, energies and momenta.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con