1996/07/31 by Viktor Abramov
Physics and Astronomy · #hep-th
published as Proc. Estonian Acad. Sci. Phys. Math., 45, 2/3, 174-182, 1996 · 10 pages
arxiv created 1996/07/31 · arxiv updated 2009/11/30
We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula of a change of variables is proved. In analogy with the fermion integral we define an analogue of the Pfaffian for a cubic matrix by means of Gaussian type integral and calculate its explicit form in the case of N=3.