Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic Map of Three-Channel S Matrix -Generalized Uniformization and
  Mittag-Leffler Expansion-   We explore the analytic structure of the three-channel $S$ matrix by
generalizing uniformization and making a single-valued map for the
three-channel $S$ matrix. First, by means of the inverse Jacobi's elliptic
function we construct a transformation from eight Riemann sheets of the
center-of-mass energy squared complex plane onto a torus, on which the
three-channel $S$ matrix is represented single-valued. Secondly, we show that
the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering
amplitude includes not only topologically trivial but also nontrivial
contributions and is given by the Weierstrass zeta function. Finally, we
examine the obtained formula in the context of a simple three-channel model.
Taking a simple non-relativistic effective field theory with contact
interaction for the $S=-2$, $I=0$, $J^P = 0^+$,
$\Lambda\Lambda-N\Xi-\Sigma\Sigma$ coupled-channel scattering, we demonstrate
that the scattering amplitude as a function of the uniformization variable is,
in fact, given by the Mittag-Leffler expansion with the Weierstrass zeta
function and that it is dominated by contributions from neighboring poles.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
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
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom