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Symplectic geometry?

  1. Nov 28, 2007 #1
    How crucial is symplectic geometry to fundamental physics?

    Any examples? I know it is related to string theory.
  2. jcsd
  3. Nov 28, 2007 #2


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    Symplectic Geometry underlies Hamiltonian Mechanics and Optics.

    http://www.math.hawaii.edu/~gotay/Symplectization.pdf [Broken]
    Last edited by a moderator: May 3, 2017
  4. Nov 29, 2007 #3
    Just read the article. They sound very promising but 15 years, sympletic geometry still hasn't got much attention.
  5. Nov 30, 2007 #4


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    What time scale is more appealing to you?
    ...Gotten the attention from whom?

    Here's a more recent article:
    http://www.math.princeton.edu/~acannas/04_SG/ [Broken]
    Last edited by a moderator: May 3, 2017
  6. Nov 30, 2007 #5
    The first article was making huge claims about symplectic geometry but I don't see them happening. The title of the article 'Symplectization of Science' was too catchy.
  7. Nov 30, 2007 #6


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    Every known (or maybe even conceivable) system of classical mechanics can be cast in the form of symplectic geometry.
    Poisson after whom the bracket that introduces the symplectic structure on phase space is named, died in 1840. Through Hamiltons recasting of the equations of motion as the flow of a vectorfield induced by an observable and a symplectic structure, through the Noether theorems, Heisenbergs quantization, Diracs cannonical analysis of gauge systems to todays work on the interpretation of Quantum Gravity, symplectic structures have provided the foundation (sometimes implicitly) of almost the entire apparatus of mechanics for the last century and a half at least.
  8. Nov 30, 2007 #7
    How crucial is it to learn symplectic geometry if one wants to understand string theory?
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