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Quantum mechanics on profinite groups and partial order

no / Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group Z(p) and momenta in the group Q(p)/Z(p), and a quantum system with positions in the profinite group (Z) over cap and momenta in the group Q/Z. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T-0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T-0-topologies, in a quantum mechanical context, is discussed.

Identiferoai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/9748
Date January 2013
CreatorsVourdas, Apostolos
Source SetsBradford Scholars
Detected LanguageEnglish
TypeArticle, No full-text available in the repository

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