Strict deformation quantization and local spin interactions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910491503230976 |
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| author | Drago, Nicolò van de Ven, Christiaan J. F. |
| author_facet | Drago, Nicolò van de Ven, Christiaan J. F. |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10697 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strict deformation quantization and local spin interactions Drago, Nicolò van de Ven, Christiaan J. F. Mathematical Physics Operator Algebras 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. 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. |
| title | Strict deformation quantization and local spin interactions |
| topic | Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2210.10697 |