Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I.
  One, Two, and Three Particles   This is the first in a pair of articles that classify the configuration space
and kinematic symmetry groups for $N$ identical particles in one-dimensional
traps experiencing Galilean-invariant two-body interactions. These symmetries
explain degeneracies in the few-body spectrum and demonstrate how tuning the
trap shape and the particle interactions can manipulate these degeneracies. The
additional symmetries that emerge in the non-interacting limit and in the
unitary limit of an infinitely strong contact interaction are sufficient to
algebraically solve for the spectrum and degeneracy in terms of the
one-particle observables. Symmetry also determines the degree to which the
algebraic expressions for energy level shifts by weak interactions or
nearly-unitary interactions are universal, i.e.\ independent of trap shape and
details of the interaction. Identical fermions and bosons with and without spin
are considered. This article sequentially analyzes the symmetries of one, two
and three particles in asymmetric, symmetric, and harmonic traps; the sequel
article treats the $N$ particle case.

36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th