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arXiv · 2503.04938

Topological description of pure invariant states of the Weyl $C^*$-algebra

Giuseppe De Nittis·Santiago G. Rendel
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Abstract

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.

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Giuseppe De Nittis, Santiago G. Rendel. 2025-03-06. Topological description of pure invariant states of the Weyl $C^*$-algebra. https://arxiv.org/abs/2503.04938

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