Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear supersymmetry in the quantum Calogero model   It is long known that the rational Calogero model describing n identical
particles on a line with inverse-square mutual interaction potential is quantum
superintegrable. We review the (nonlinear) algebra of the conserved quantum
charges and the intertwiners which relate the Liouville charges at couplings g
and g+1. For integer values of g, these intertwiners give rise to additional
conserved charges commuting with all Liouville charges and known since the
1990s. We give a direct construction of such a charge, the unique one being
totally antisymmetric under particle permutations. It is of order
n(n-1)(2g-1)/2 in the momenta and squares to a polynomial in the Liouville
charges. With a natural Z_2 grading, this charge extends the algebra of
conserved charges to a nonlinear supersymmetric one. We provide explicit
expressions for intertwiners, charges and their algebra in the cases of two,
three and four particles.

0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int