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Title: Quantum group and the Lie-Admissible Q-algebra

Abstract

In the present paper the author proves that the deformation q-Lie algebra is a particular case of Lie-Admissible Q-algebra. With the help of Fock representation of the new operators A and A{sup +} he can find the eigenvalues of the corresponding non-canonical harmonic oscillator. Also the eigenvalues of the q-deformed harmonic oscillator are found and then can be used for the calculation of the masses of several particles. From the boson realization of the operations A and A{sup +} he can define generalized non-canonical commutation relations between the operator J{sub {plus minus}}, J{sub z} and construct the quantum group SU(2){sub Q,q}. The special case Q = q{sup {minus}1} corresponds exactly to SU(2)q quantum group.

Authors:
 [1]
  1. Univ. of Patras (Greece) Inst. for Basic Research, Palm Harbor, FL (United States)
Publication Date:
OSTI Identifier:
7206190
Resource Type:
Journal Article
Journal Name:
Hadronic Journal; (United States)
Additional Journal Information:
Journal Volume: 14:3; Journal ID: ISSN 0162-5519
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM MECHANICS; GROUP THEORY; BOSONS; COMMUTATION RELATIONS; EIGENVALUES; ELEMENTARY PARTICLES; FOCK REPRESENTATION; HADRONS; HARMONIC OSCILLATORS; LIE GROUPS; MASS; MATHEMATICAL OPERATORS; ELECTRONIC EQUIPMENT; EQUIPMENT; MATHEMATICS; MECHANICS; OSCILLATORS; SYMMETRY GROUPS; 661100* - Classical & Quantum Mechanics- (1992-); 662100 - General Theory of Particles & Fields- (1992-)

Citation Formats

Jannussis, A. Quantum group and the Lie-Admissible Q-algebra. United States: N. p., 1991. Web.
Jannussis, A. Quantum group and the Lie-Admissible Q-algebra. United States.
Jannussis, A. Sat . "Quantum group and the Lie-Admissible Q-algebra". United States.
@article{osti_7206190,
title = {Quantum group and the Lie-Admissible Q-algebra},
author = {Jannussis, A},
abstractNote = {In the present paper the author proves that the deformation q-Lie algebra is a particular case of Lie-Admissible Q-algebra. With the help of Fock representation of the new operators A and A{sup +} he can find the eigenvalues of the corresponding non-canonical harmonic oscillator. Also the eigenvalues of the q-deformed harmonic oscillator are found and then can be used for the calculation of the masses of several particles. From the boson realization of the operations A and A{sup +} he can define generalized non-canonical commutation relations between the operator J{sub {plus minus}}, J{sub z} and construct the quantum group SU(2){sub Q,q}. The special case Q = q{sup {minus}1} corresponds exactly to SU(2)q quantum group.},
doi = {},
journal = {Hadronic Journal; (United States)},
issn = {0162-5519},
number = ,
volume = 14:3,
place = {United States},
year = {1991},
month = {6}
}