Diagrams in classical and semiclassical perturbation theory

DOI10.1063/1.532273zbMath1004.37065OpenAlexW2088884757MaRDI QIDQ4260542

Panayotis Panayotaros

Publication date: 16 December 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532273

zbMATH Keywords

hydrodynamicsclassical mechanicsdiagrammatic methodPoincaré-Birkhoff normal formsquantum diagrams

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Normal forms for dynamical systems (37G05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dynamical systems in classical and celestial mechanics (37N05) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Cites Work

• The Schrödinger equation and canonical perturbation theory
• Symbolic computation of derivations using labelled trees
• Quantization of the classical Lie algorithm in the Bargmann representation
• Gravity waves on the surface of the sphere
• Lie series and invariant functions for analytic symplectic maps
• Uniform Nekhoroshev estimates on quantum normal forms
• Canonical transformations depending on a small parameter

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