Physics NotePublished
On the Classification of <math>N</math>-extended Supersymmetric Quantum Mechanical Systems
A. Pashnev; F. Toppan
2000
Publication details
- Authors
- A. Pashnev; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 2000
- Description
- In this paper some properties of the irreducible multiplets of representation for the <math>N = ( p, q )</math> - extended supersymmetry in one dimension are discussed. Essentially two results are here presented. At first a peculiar property of the one dimension is exhibited, namely that any multiplet containing <math>2d</math> (<math>d</math> bosonic and <math>d</math> fermionic) particles in <math>M</math> different spin states, is equivalent to a {'''d,d'''} multiplet of just ''2'' spin states (all bosons and all fermions being grouped in the same spin). Later, it is shown that the classification of all multiplets of this kind carrying an irreducible representation of the <math>N</math> - extended supersymmetry is in one-to-one correspondence with the classification of real-valued Clifford <math>\Gamma</math>-matrices of Weyl type. In particular, <math>p+q</math> is mapped into <math>D</math>, the space-time dimensionality, while <math>2d</math> is determined to be the dimensionality of the corresponding <math>\Gamma</math>-matrices. The implications of these results to the theory of spinning particles are analyzed.
- Year
- 2000
- Number
- CBPF-NF-029/00
- Linked to a thesis
- No
- Linked to a grant
- No