Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the origin of the correspondence between classical and quantum
  integrable theories   We show how functional relations, which can be considered as a definition of
a quantum integrable theory, entail an integral equation that can be extended
upon introducing dynamical variables to a Marchenko-like equation. Then, we
naturally derive from the latter a classical Lax pair problem. We exemplify our
method by focusing on the massive version of the ODE/IM (Ordinary Differential
Equations/Integrable Models) correspondence involving the sinh-Gordon model,
first emerged in the gauge theories and scattering amplitudes/Wilson loops
$AdS_3$ context with many moduli/masses, but in a way which reveals its
generality. In fact, we give some hints, in the end, to its application to spin
chains.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph