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Quantum Deformations of Relativistic Symmetries
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تأليف
V.N. Tolstoy
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ننا ناقشنا تشويهات الكم الخاصة بالألجبرا والبوينكار الذي يحتوي على أربعة أبعاد. في حالة الألجبرا البوينكار، تم إظهار أن أغلب الr-matrices الكلاسيكية من تصنيف س. زاكرزفسكي يتعلقون بالتشويهات المثلثة من النوع الأبلياني والأردني. وتم إعطاء جزء من التشويهات المتعلقة بr-matrices من تصنيف زاكرزفسكي بشكل واضح.
We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types. A part of twists corresponding to the r-matrices of Zakrzewski classification are given in explicit form.
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We discussed twisted quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S.Zakrzewski classification can be presented as a sum of subordinated r-matrices of Ab
elian and Jordanian types. Corresponding twists describing quantum deformations are obtained in explicit form. This work is an extended version of the paper url{arXiv:0704.0081v1 [math.QA]}.
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The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry i
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