On quantum mechanics and generalized Clifford algebras |
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Authors: | A K Kwaśniewski W Bajguz I Jaroszewski |
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Institution: | (1) Computer Science Laboratory ul. Sosnowa 64 Institute of Physics, Bialystok University, PL-15-887 Bialystok, POLAND;(2) College of Applied Mathematics and Computer Science, Czysta 11, PL-15-463 Bialystok |
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Abstract: | In this note we give elementary examples of the naturalness of generalized Clifford algebras appearance, in some particular
quantum mechanical models.
First Weyl’s program 1] for quantum kinematics for the case of simplest Galois fieldsZ
n
is realized in terms of generalized Clifford algebras. Dynamics might then be introduced, following the ideas of Hanney and
Berry 2], as shown in 3].
Second the coherent state picture of the finite dimensional “Z
n
— Quantum Mechanics” is presented.
In the last part the known coherent states ofq-deformed quantum oscillators (q≡ω) are explicitly shown in the generalized Grassman algebras and the generalized Clifford algebras settings.
Presented atThe Polish-Mexican Seminar, Kazimierz Dolny, August 1998 — Poland. 176 |
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Keywords: | |
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