Foundations of calculus on super euclidean space rm|n based on a Frechet-Grassmann algebra

Atsushi Inoue, Yoshiaki Maeda

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)


    We define a Frechet-Grassmann algebra with infinitely many generators as the supernumber algebra. Using this, we define a so-called super Euclidean space and may develop elementary analysis on it. In doing this, we clarify the relation between Grassmann generators and odd variables. Moreover, we construct a certain Hamilton flow on the super Euclidean space, corresponding to the ‘classical’ orbit of the Pauli equation, for which we define the action integral, van Vleck determinant etc. as similar as we do on the Euclidean space.

    Original languageEnglish
    Pages (from-to)72-112
    Number of pages41
    JournalKodai Mathematical Journal
    Issue number1
    Publication statusPublished - 1991 Jan 1

    ASJC Scopus subject areas

    • Mathematics(all)

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