## A Clifford Algebra Realization of Supersymmetry and Its Polyvector Extension in Clifford Spaces

**Authors:** Carlos Castro

It is shown explicitly how to construct a novel (to our knowledge)
realization of the Poincare superalgebra in 2D. These results can be extended
to other dimensions and to (extended) superconformal and (anti)
de Sitter superalgebras. There is a fundamental difference between the
findings of this work with the other approaches to Supersymmetry (over
the past four decades) using Grassmannian calculus and which is based on
anti-commuting numbers. We provide an algebraic realization of the anticommutators
and commutators of the 2D super-Poincare algebra in terms
of the generators of the tensor product Cl1,1(R) x
A of a two-dim Clifford
algebra and an internal algebra A whose generators can be represented
in terms of powers of a 3 x 3 matrix Q, such that Q3 = 0. Our realization
differs from the standard realization of superalgebras in terms
of differential operators in Superspace involving Grassmannian (anticommuting)
coordinates θ^{α} and bosonic coordinates x^{μ}. We conclude in
the final section with an analysis of how to construct Polyvector-valued extensions
of supersymmetry in Clifford Spaces involving spinor-tensorial supercharge
generators Qμ1μ2.....μn
and momentum polyvectors Pμ1μ2....μn.
Clifford-Superspace is an extension of Clifford-space and whose symmetry
transformations are generalized polyvector-valued supersymmetries.

**Comments:** 15 pages, submitted to Foundations of Physics.

**Download:** **PDF**

### Submission history

[v1] 26 Jun 2010

**Unique-IP document downloads:** 397 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*