Supersymmetry without Grassmann variables

Supersymmetry without Grassmann variables

Grassmann Variables in Jordan Matrix Models

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables solidifies the relationship between supersymmetry and triality.

Description of Vorticity by Grassmann Variables and an Extension to Supersymmetry

Hagen Kleinert’s early interest in particle physics quantum field theory served him well for his subsequent researches on statistical physics and collective phenomena. Therefore, on the occasion of a significant birthday, I offer him this essay, in which particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann va...

Fermions and world-line supersymmetry

The world-line path-integral representation of fermion propagators is discussed. Particular attention is paid to the representation of γ5, which is connected to the realization of manifest world-line supersymmetry. Contribution to Proceedings of 29th Int. Symposium on the Theory of Elementary Particles Buckow (1995) Introduction The path-integral representation of the evolution operator of dyna...

Paragrassmann Integral, Discrete Systems and Quantum Groups

This report is based on review paper [1]. Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the Z p+1 Potts model on a chain. Finite dimensional paragrassmann representations for GL q (2) are constructed. Generalizations of grassmann al...