Topological description of pure invariant states of the Weyl $C^*$-algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | De Nittis, Giuseppe Rendel, Santiago G. |
| author_facet | De Nittis, Giuseppe Rendel, Santiago G. |
| contents | In this work we study the topology of certain families of states of the Weyl $C^*$-algebra with finite degrees of freedom. We focus on families of pure states characterized by symmetries and a (semi-)regularity condition, and obtain precise topological descriptions through homeomorphisms with other explicit spaces. Of special importance are the families of pure, semi-regular states invariant under either continuous (plane-wave states) or discrete (Bloch-wave states) spatial translations, and the family of states invariant under discrete, mutually commuting spatial and momentum translations (Zak-wave states), all of which we completely characterize. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological description of pure invariant states of the Weyl $C^*$-algebra De Nittis, Giuseppe Rendel, Santiago G. Mathematical Physics Operator Algebras Primary: 46L30, Secondary: 81R15, 81P16, 81R10 In this work we study the topology of certain families of states of the Weyl $C^*$-algebra with finite degrees of freedom. We focus on families of pure states characterized by symmetries and a (semi-)regularity condition, and obtain precise topological descriptions through homeomorphisms with other explicit spaces. Of special importance are the families of pure, semi-regular states invariant under either continuous (plane-wave states) or discrete (Bloch-wave states) spatial translations, and the family of states invariant under discrete, mutually commuting spatial and momentum translations (Zak-wave states), all of which we completely characterize. |
| title | Topological description of pure invariant states of the Weyl $C^*$-algebra |
| topic | Mathematical Physics Operator Algebras Primary: 46L30, Secondary: 81R15, 81P16, 81R10 |
| url | https://arxiv.org/abs/2503.04938 |