TY - JOUR

T1 - Foundations of calculus on super euclidean space rm|n based on a Frechet-Grassmann algebra

AU - Inoue, Atsushi

AU - Maeda, Yoshiaki

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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.

AB - 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.

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U2 - 10.2996/kmj/1138039340

DO - 10.2996/kmj/1138039340

M3 - Article

AN - SCOPUS:84887246836

VL - 14

SP - 72

EP - 112

JO - Kodai Mathematical Journal

JF - Kodai Mathematical Journal

SN - 0386-5991

IS - 1

ER -