Three-point non-associative supersymmetry generalization

Abstract

We consider a non-associative generalization of supersymmetry based on three-point associators like $\left[Q_x,Q_y,Q_z\right]$ for $Q_{a,\dot{a}}$ supersymmetric generators. Such associators are connected with the products of $Q_{a,\dot{a}}$ and $x_{b\dot{b}}$. We: (a) calculate Jacobiators and show that the Jacobiators can be zero with some choice of corresponding coefficients in associators; (b) perform dimensional analysis for the coefficients in associators; (d) calculate some commutators involving coordinates and momentums; (e) estimate the weakness of non-associativity.

arXiv commentessential changes in the text