Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Holomorphic Realization of Non-Commutative Space-Time and Gauge Invariance(IOP Publishing, 2003) Mir-Kasimov, Rufat M.The realization of the Poincare Lie algebra in terms of noncommutative differential calculus over the commutative algebra of functions is considered. The algebra of functions is defined on the spectrum of the unitary irreducible representations of the De Sitter group. Corresponding space-time carries the noncommutative geometry. Gauge invariance principle consistent with this noncommutative space is considered.Conference Object Citation - WoS: 1Citation - Scopus: 1The Newton-Wigner Localization Concept and Noncommutative Space(Springer Verlag, 2005) Mir-Kasimov, Rufat M.In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme.Conference Object On Classical and Quantum Q-Oscillators in the Relativistic Theory(Springer Verlag, 2004) Mir-Kasimov, Rufat M.The factorization method, applied to the finite-difference Schrödinger equation in the relativistic configurational space, allows to consider the q-deformations as a relativistic effect. In particular, different factorizations allow to obtain all known q-oscillators in a unified way. The classical limit of deformed Hamiltonians is investigated.Article Citation - WoS: 10Citation - Scopus: 9Q-Deformed and C-Deformed Harmonic Oscillators(Yukawa Institute for Theoretical Physics, 2003) Sogami, Ikuo S.; Koizumi, Kouzou; Mir-Kasimov, Rufat M.Hamilton functions of classical deformed oscillators (c-deformed oscillators) are derived from Hamiltonians of g-deformed oscillators of the Macfarlane and Dubna types. A new scale parameter, lq, with the dimension of length, is introduced to relate a dimensionless parameter characterizing the deformation with the natural length of the harmonic oscillator. Contraction from q-deformed oscillators to c-deformed oscillators is accomplished by keeping lq finite while taking the limit ℏ → 0. The c-deformed Hamilton functions for both types of oscillators are found to be invariant under discrete translations: the step of the translation for the Dubna oscillator is half of that for the Macfarlane oscillator. The c-deformed oscillator of the Macfarlane type has propagating solutions in addition to localized ones. Reinvestigation of the g-deformed oscillator carried out in the light of these findings for the c-deformed systems proves that the g-deformed systems are invariant under the same translation symmetries as the c-deformed systems and have propagating waves of the Bloch typeArticle Citation - WoS: 9Citation - Scopus: 10Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation(Springer Verlag, 2002) Mir-Kasimov, Rufat M.A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich-Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.