Supersymmetry from a braided point of view

Abstract

We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and covariant derivative are obtained in the limit in question as the left and right derivatives of the calculus on the braided line.Comment: LateX file. 10 pages. To appear in Phys. Lett.

A braided interpretation of fractional supersymmetry in higher dimensions

“…Thus when q is a root of unity (q = 1) the braided Hopf algebra A is finite dimensional, having two independent elements θ (1) and θ (n) besides the identity. The dual K is also finite dimensional, but it has only one independent element D…”

“…The results of [1,2,3,4] can also be derived from a different and in some ways mathematically nicer point of view. Our work here uses a technique similar to that employed by G.I.…”

“…In four recent papers [1,2,3,4] the properties of the braided line [5,6] when its deformation parameter is a root of unity were discussed. Most notably these studies led to a novel understanding of one dimensional supersymmetry and fractional supersymmetry [7,8,9].…”

Braided oscillators

“…Braided group theory (a self contained review can be found in 4 ) deforms the notion of tensor product (called braided tensor product) and hence deforms the independence of the objects. Although braided groups arise in the formulation of quantum group covariant structures, the idea of braiding can be used without any reference to quantum groups to generalize the statistics 5 .…”

“…The actions of the generators on the Hilbert space are given by a | n = a n | n − 1 a * | n = a * n+1 | n + 1 (5) q N | n = q n | n .…”