Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-07-31
Proc. Estonian Acad. Sci. Phys. Math., 45, 2/3, 174-182, 1996
Physics
High Energy Physics
High Energy Physics - Theory
10 pages
Scientific paper
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.
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