A Clifford Algebra Realization of Supersymmetry and its Polyvector Extension in Clifford Spaces

Abstract:

It is shown explicitly how to construct a novel (to our knowledge) realization of the Poincaré 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-Poincaré algebra in terms of the generators of the tensor product Cl1,1(R) ⊗ A of a two-dim Clifford algebra and an internal algebra A whose generators can be represented in terms of powers of a 3 × 3 matrix Q such that Q3. Our realization differs from the standard realization of superalgebras in terms of differential operators in Superspace involving Grassmannian (anti-commuting) coordinates θα and bosonic coordinates xμ. 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 Qαμ1μ2...μand momentum polyvectors Clifford-Superspace is an extension of Clifford-space and whose symmetry transformations are generalized polyvector-valued supersymmetries. © 2011 Springer Basel AG.

Año de publicación:

2011

Keywords:

• Clifford algebras
• M, F theory superalgebras
• supersymmetry
• polyvector-supersymmetry

Fuente:

scopus