--- title: "On the Classification of N-extended Supersymmetric Quantum Mechanical Systems • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb3a3" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~T24gdGhlIENsYXNzaWZpY2F0aW9uIG9mIDxtYXRoPk48L21hdGg-LWV4dGVuZGVkIFN1cGVyc3ltbWV0cmljIFF1YW50dW0gTWVjaGFuaWNhbCBTeXN0ZW1z%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~QS4gUGFzaG5ldjsgRi4gVG9wcGFu%2Cdetalhe_2000%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIzYTMi%2Cs_OlRKTBo4-vdNwGIn.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "On the Classification of N-extended Supersymmetric Quantum Mechanical Systems • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~T24gdGhlIENsYXNzaWZpY2F0aW9uIG9mIDxtYXRoPk48L21hdGg-LWV4dGVuZGVkIFN1cGVyc3ltbWV0cmljIFF1YW50dW0gTWVjaGFuaWNhbCBTeXN0ZW1z%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~QS4gUGFzaG5ldjsgRi4gVG9wcGFu%2Cdetalhe_2000%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIzYTMi%2Cs_OlRKTBo4-vdNwGIn.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **On the Classification of \N\-extended Supersymmetric Quantum Mechanical Systems** **A. Pashnev; F. Toppan** 2000 [**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb3a3/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=On%20the%20Classification%20of%20%3Cmath%3EN%3C%2Fmath%3E-extended%20Supersymmetric%20Quantum%20Mechanical%20Systems) ## **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
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