# Strict deformation quantization and local spin interactions

October 19, 2022

We define a strict deformation quantization which is compatible with any
Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a
spin chain with periodic boundary conditions. This is a generalization of
previous results known for mean-field theories. The main idea is to study the
asymptotic properties of a suitably defined algebra of sequences invariant
under the group generated by a cyclic permutation. Our point of view is similar
to the one adopted by Landsman, Moretti and van de Ven, who considered a strict
deformation quantization for the case of mean-field theories. However, the
methods for a local spin interaction are considerably more involved, due to the
presence of a strictly smaller symmetry group.

Keywords:

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