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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)

[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

[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

[en] The authors realize the Jordan-Schwinger construction for the Hopf algebra U_pq(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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[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