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    Quantum mechanics on profinite groups and partial order

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    Publication date
    2013
    Author
    Vourdas, Apostolos
    Keyword
    General ultrametric space
    ; P-adic numbers
    ; Discrete wigner function
    ; Systems
    ; Fields
    ; Factorisation
    ; Weyl
    Peer-Reviewed
    yes
    
    Metadata
    Show full item record
    Abstract
    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.
    URI
    http://hdl.handle.net/10454/9748
    Version
    No full-text available in the repository
    Citation
    Vourdas A (2013) Quantum mechanics on profinite groups and partial order. Journal of Physics A: Mathematical and Theoretical. 46(4)
    Link to publisher’s version
    http://dx.doi.org/10.1088/1751-8113/46/4/043001
    Type
    Article
    Collections
    Engineering and Informatics Publications

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