Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many Body Problems with "Spin"-Related Contact Interactions   We study quantum mechanical systems with "spin"-related contact interactions
in one dimension. The boundary conditions describing the contact interactions
are dependent on the spin states of the particles. In particular we investigate
the integrability of $N$-body systems with $\delta$-interactions and point spin
couplings. Bethe ansatz solutions, bound states and scattering matrices are
explicitly given. The cases of generalized separated boundary condition and
some Hamiltonian operators corresponding to special spin related boundary
conditions are also discussed.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th