Nonlinear reformulation of Heisenberg's dynamics

DOI10.1007/s10773-005-7048-9zbMath1104.81069arXivquant-ph/0210198OpenAlexW1985835968MaRDI QIDQ2505954

Martin Ziegler, Benno Fuchssteiner

Publication date: 28 September 2006

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0210198

zbMATH Keywords

integrabilitysymplectic manifoldsquantum mechanicsnonlinear symmetriesHeisenberg's picture

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Geometry and quantization, symplectic methods (81S10) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (1)

Noncommutative Korteweg–de Vries and modified Korteweg–de Vries hierarchies via recursion methods

Cites Work

• Properties of infinite dimensional Hamiltonian systems
• Reduction of symplectic manifolds with symmetry
• Algorithmic determination of infinite-dimensional symmetry groups for integrable systems in \(1+1\) dimensions
• Korteweg-de Vries equation: a completely integrable Hamiltonian system
• Minimal Identities of Symmetric Matrices
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
• On the integrability of quantum mechanics as an infinite dimensional Hamiltonian system
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