Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sum rules for spin-$1/2$ quantum gases in states with well-defined
  spins: II. Spin-dependent two-body interactions   Sums of matrix elements of spin-dependent two-body momentum-independent
interactions and sums of their products are calculated analytically in the
basis of many-body states with given total spin --- the states built from spin
and spatial wavefunctions belonging to multidimensional irreducible
representations of the symmetric group, unless the total spin has the maximal
allowed value. As in the first part of the series [V. A. Yurovsky, Phys. Rev. A
91, 053601 (2015)], the sum dependence on the many-body states is given by
universal factors, which are independent of the Hamiltonians of non-interacting
particles. The sum rules are applied to perturbative analysis of energy spectra
and to calculation of two-body spin-dependent local correlations.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph