Introductive backgrounds to modern quantum mathematics with application to nonlinear dynamical systems - Prykarpatsky, Anatoliy K.; Bogoliubov, Nikolai N., Jr.; Golenia, Jolanta; Taneri, Ufuk (Springer/Plenum Publishers, 2008)
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.
Keywords: quantum mathematics; creation and annihilation operators; Bogolubof functional equation; nonlinear dynamical systems; fock space imbedding method; C*-algebra representations