Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems |
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| Authors: | Anatoliy K. Prykarpatsky,Nikolai N. Bogoliubov Suffix" >Jr.,Jolanta Golenia,Ufuk Taneri |
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| Affiliation: | 1.The AGH University of Science and Technology,Kraków,Poland;2.Department of Mathematical Physics,Institute of Mathematics of NAS,Kiev,Ukraine;3.The Abdus Salam International Center for Theoretical Physics,Trieste,Italy;4.V.A. Steklov Mathematical Institute of RAN,Moscow,Russia;5.Dept. of Applied Mathematics,The AGH University of Science and Technology,Kraków,Poland;6.Department of Applied Mathematics and Computer Science,Eastern Mediterranean University EMU,Famagusta,North Cyprus;7.Institute of Graduate Studies,North Cyprus and Kyrenia American University GAU,Kyrenia,North Cyprus |
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| Abstract: | Introductive backgrounds to a new mathematical physics discipline—Quantum Mathematics—are discussed and analyzed both from historical and from analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. The Authors devote their article to their Friend and Teacher academician Prof. Anatoliy M. Samoilenko on occasion of his 70 years-Birthday with great compliments and gratitude to his brilliant talent and impressive impact to modern theory of nonlinear dynamical systems of mathematical physics and nonlinear analysis |
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| Keywords: | Quantum mathematics Creation and annihilation operators Bogolubof functional equation Nonlinear dynamical systems Fock space imbedding method C*-algebra representations |
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