Physics NotePublished
Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics
Zhanna Kuznetsova; M. Rojas; F. Toppan
Publication details
- Authors
- Zhanna Kuznetsova; M. Rojas; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 14/07/2010
- Description
- the noWe present an algorithmic classification of the irreps of the $N$-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields. Based on the $1$-to-$1$ \cite{pt} correspondence between Weyl-type Clifford algebras (whose irreps are fully classified) and classes of irreps of the $N$-extended $1D$ supersymmetry, we are able to prove that, for $N=3,5\quad mod \quad 8$, two classes of irreps, real and quaternionic, are found. \par The complete classification of irreps is presented up to $N\leq 10$. The fields of an irrep are accommodated in $l$ different spin states. $N=10$ is the minimal value admitting length $l>4$ irreps. The classification of length-$4$ irreps of the $N=12$ and {\em real} $N=11$ extended supersymmetries is also explicitly presented.\par Tensoring irreps allows us to systematically construct manifestly ($N$-extended) supersymmetric multi-linear invariants {\em without} introducing a superspace formalism. Multi-linear invariants can be constructed both for {\em unconstrained} and {\em multi-linearly constrained} fields. Examples are given.\par Tensoring zero-energy irreps leads us to tion of the {\em fusion algebra} of the $1D$ $N$-extended supersymmetric vacua.
- Year
- 2005
- Number
- CBPF-NF-010/05
- Linked to a thesis
- No
- Linked to a grant
- No