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1974; 8 p; 3 refs.
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1 Mar 1972; 361 p
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[en] Two types of operators (I,II) are constructed in terms of bosonic quantum (q-)oscillator operators. These operators satisfy a relation analogous to the q-commutation relation for fermionic quantum (q-)oscillators. Both types of operators (I,II) can be identified with the fermionic harmonic oscillator in the limit q→1 by exploiting the presence of certain arbitrary functions of the deformation parameter q. For I they may be identified as parameters of U (1) transformations while for II they correspond to parameters of GL(2,R) transformations. Appropriate fermionic number operators in the limit q→1 are also considered. (author)
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15 refs.
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[en] The analytical solutions of two kinds of Raman-Nath-type equations are found by a method which avoids recourse to techniques of operatorial time-ordering and is based instead on two special cases of the dual of the Baker-Campbell-Hausdorff formula
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[en] In this paper the continuum eigenfunctions and eigenvalue spectra for a generalized two-mode squeeze operator are constructed. Our analyses also show explicitly that proper eigenstates of the generalized two-mode squeeze operator do not exist, which implies that the generalized two-mode squeeze operator does not have a discrete spectrum
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[en] The authors realize the Jordan-Schwinger construction for the Hopf algebra Upq(su(2)). They then calculate the creation and annihilation tensor operators together with their tensor products including the Casimir operators. 15 refs., 3 fig
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25 Feb 1972; 627 p
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Reports on Mathematical Physics; v. 3 p. 201-207
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J. Math. Phys. (N.Y.); v. 14(9); p. 1199-1201
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[en] Generalized permutation relation determined by a set of coefficients μ=(μ1,...,μsub(k)) are under consideration for a pair of operators a and a+ conjugated to each other. The totality of operator functions of a and a+ (the μ-algebra) is investigated. It is shown that a and a+ can be interpreted as the annihilation and creation operators of some 'particles'. Unlike the well known types of the quantization of Bose-Einstein and Fermi-Dirac the μ-quantization generally violates the proportionality between the energy of a state and its number of 'particles', a fact which is treated as a certain interaction between the 'particles'. All the particular cases of μ-quantization free from interaction are determined
[fr]
On considere les relations de permutation generalisees determinees par un ensemble de coefficients μ=(μ1,...,μsub(k)), pour un couple d'operateurs a et a+ adjoints l'un de l'autre. On etudie les familles des operateurs (μ-algebres) fonctions de a et a+. Il est montre que a et a+ peuvent etre interpretes comme operateurs d'annihilation et de creation de certaines 'particules'. Contrairement aux types de quantification de Bose-Einstein et de Fermi-Dirac bien connus, la μ-quantification viole, en general, la proportionnalite entre l'energie d'un etat et son nombre de 'particules' ce qu'on peut interpreter comme une certaine interaction des 'particules'. Tous les cas particuliers de la μ-quantification, ou l'interaction n'a pas lieu, sont determinesOriginal Title
Operateurs quantiques generalises de creation et d'annihilation
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Annales de la Fondation Louis de Broglie; v. 5(2); p. 111-125
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