The 'symplectic camel principle' and semiclassical mechanics

@article{Gosson2002TheC,
  title={The 'symplectic camel principle' and semiclassical mechanics},
  author={M. D. Gosson},
  journal={Journal of Physics A},
  year={2002},
  volume={35},
  pages={6825-6851}
}
  • M. D. Gosson
  • Published 2002
  • Mathematics
  • Journal of Physics A
    • We propose a theory of semiclassical mechanics in phase space based on the notion of quantized symplectic area. The definition of symplectic area makes use of a deep topological property of symplectic mappings, known as the 'principle of the symplectic camel' which places stringent conditions on the global geometry of Hamiltonian mechanics. Following this principle, symplectic mappings—and hence Hamiltonian flows—are much more rigid than Liouville's theorem suggests. The dynamical objects of… CONTINUE READING
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    27 Citations
    Background Citations
    14
    Methods Citations
    4
    Results Citations
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    27 Citations
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    Citation Type

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    References

    SHOWING 1-10 OF 27 REFERENCES
    The symplectic camel and phase space quantization
    • 31
    Symplectic Invariants and Hamiltonian Dynamics
    • 756
    The meaning of Maslov's asymptotic method: The need of Planck's constant in mathematics
    • 13
    • PDF
    Chaos in classical and quantum mechanics
    • 3,029
    Symplectic geometry and analytical mechanics
    • 924
    The Geometry of Physics
    • 275
    Semiclassical Trace Formulas in Terms of Phase Space Path Integrals
    • 20
    • PDF
    Corrected bohr-sommerfeld quantum conditions for nonseparable systems
    • 464
    • PDF
    Techniques and Applications of Path Integration
    • 1,839
    Pseudo holomorphic curves in symplectic manifolds
    • 2,043
    • PDF