Cover Image

Quantum mathematics: backgrounds and some applications to nonlinear dynamical systems

Backgrounds of a new mathematical physics discipline ’Quantum Mathematics’ are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1934, are demonstrated, and an impressive applica...

Full description

Saved in:

Bibliographic Details
Published in:	Нелінійні коливання
Date:	2008
Main Authors:	Bogolubov, N.N., Golenia, J., Prykarpatsky, A.K., Taneri, U.
Format:	Article
Language:	English
Published:	Інститут математики НАН України 2008
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/178153
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:	Quantum mathematics: backgrounds and some applications to nonlinear dynamical systems / N.N. Bogolubov, J. Golenia, A.K. Prykarpatsky, U. Taneri // Нелінійні коливання. — 2008. — Т. 11, № 1. — С. 7-20. — Бібліогр.: 31 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

Similar Items

Generalized de Rham – Hodge complexes, the related characteristic Chern classes and some applications to integrable multidimensional differential systems on Riemannian manifolds
by: Bogolubov, N.N., et al.
Published: (2007)

The Lagrangian and Hamiltonian analysis of some relativistic electrodynamics models and their quantization
by: Bogolubov (Jr.), N.N., et al.
Published: (2009)

On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability
by: Golenia, J., et al.
Published: (2010)

The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems
by: Prykarpatsky, A.K., et al.
Published: (2003)

The Bogolubov generating functional method in statistical physics and “collective” variables transform within the grand canonical ensemble
by: Bogolubov (jr.), N.N., et al.
Published: (2007)

Lie-algebraic structure of (2 + 1)-dimensional Lax-type integrable nonlinear dynamical systems
by: Prykarpatsky, A.K., et al.
Published: (2004)

A current algebra approach to the equilibrium classical statistical mechanics and its applications
by: Bogolubov, N., et al.
Published: (2013)

An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications
by: Prykarpatsky, A.K.
Published: (2008)

Macroscopic quantum state and high-temperature superconductivity in semi-localized 2D electron system with circular molecular orbits
by: Sugahara, M., et al.
Published: (2001)

Mathematical modeling of the state of dynamic multiplicative nonlinear systems
by: V. A. Stoian
Published: (2022)

School-Seminar «Nonlinear problems of mathematical physics and their applications»
by: Samoilenko , A. M., et al.
Published: (1992)

Some applications of mathematics of functional intervals
by: P. S. Seno
Published: (2016)

On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems
by: Prykarpatski, A.K.
Published: (2018)

Algebraic scheme of discrete approximations of linear and nonlinear dynamic systems of mathematical physics
by: Mitropolsky , Yu. A., et al.
Published: (1988)

The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme
by: Prykarpatsky, A.K., et al.
Published: (2017)

Fluctuational dynamics and the structure factor of nonlinear reactive systems on a 1D lattice
by: Gerasimov, O.I., et al.
Published: (1999)

Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole-type transformations
by: Blackmore, D., et al.
Published: (2013)

Swept volume dinamical systems and their kinetic models
by: Bogoliubov, N.N., et al.
Published: (1999)

On some applications of isometricity of functional spaces in applied mathematics
by: D. M. Bushev
Published: (2020)

Dynamical system approach to solving linear programming problems and applications in economic modelling
by: Tverdokhlib, I.P., et al.
Published: (2002)

Dynamical system approach to solving linear programming problems and applications in economic modelling
by: Tverdokhlib, I.P., et al.
Published: (2002)

Agreement of 1654: some background and consequences
by: O. Motsia
Published: (2015)

Finite-Dimensional Reductions of Conservative Dynamical Systems and Numerical Analysis. I
by: Prykarpatsky, A.K., et al.
Published: (2001)

Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
by: Gafiychuk, V.V., et al.
Published: (2004)

School-seminar “Nonlinear boundary value problems of mathematical physics and their applications”
by: Samoilenko, A. M., et al.
Published: (1990)

School-Seminar “Nonlinear boundary-value problems in Mathematical Physics and their applications”
by: Berezovsky, A. A., et al.
Published: (1996)

Mathematical modeling of nonlinear processes in the dynamics of viscoelastic plates in the gas stream
by: A. F. Verlan, et al.
Published: (2014)

The Mathematical Modeling of Some Mechanisms for Integrating Economic Systems
by: V. A. Dilenko, et al.
Published: (2018)

On the Exponential Stability of Some Nonlinear Systems
by: Persidskii, S. K., et al.
Published: (2005)

The Bogolubov representation of the polaron model and its completely integrable RPA-approximation
by: Bogolubov (jr.), N.N., et al.
Published: (2010)

On the completely integrable calogero-type discretizations of Lax-integrable nonlinear dynamical systems and related coadjoint Markov-type orbits
by: Prykarpatsky, A. K., et al.
Published: (2016)

Quantum corrections to the dynamics of the gravitational system
by: V. V. Kuzmichev, et al.
Published: (2019)

Quantum corrections to the dynamics of the gravitational system
by: V. V. Kuzmychov, et al.
Published: (2019)

Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole-type transformations
by: D. Blackmore, et al.
Published: (2013)

The Canonical Reduction Method for Symplectic Structures and Its Applications
by: Prykarpatsky, A.K., et al.
Published: (2001)

Stability of some stationary nonlinear large-scale systems
by: R. V. Mullazhonov, et al.
Published: (2017)

On the classical Maxwell–Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm
by: A. K. Prykarpatsky, et al.
Published: (2016)

On the classical Maxwell–Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm
by: A. K. Prykarpatsky, et al.
Published: (2016)

Lie-algebraic structure of (2 + 1)-dimensional Lax-type integrable nonlinear dynamical systems
by: Hentosh, О. Ye., et al.
Published: (2004)

Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
by: Hentosh, O.Ye., et al.
Published: (2019)