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

12 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 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Foundations of calculus on super euclidean space r<sup>m|n</sup> based on a Frechet-Grassmann algebra'. Together they form a unique fingerprint.

Cite this