Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics
Abstract
Description
The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional supersymmetric sigma models are constructed. The role of both Clifford algebras and the Cayley-Dickson's doublings of algebras in association with the N-extended supersymmetries is discussed. We prove in specific examples that the octonionic structure constants enter the N=8 invariant actions as coupling constants. We further explain how to relate one-dimensional supersymmetric quantum mechanical systems to the dimensional reduction of higher-dimensional supersymmetric theories.
16 pages. Talk given at the Fifth International Conference on Mathematical Methods in Physics IC2006, April 24-28 2006, CBPF, Rio de Janeiro, Brazil
16 pages. Talk given at the Fifth International Conference on Mathematical Methods in Physics IC2006, April 24-28 2006, CBPF, Rio de Janeiro, Brazil