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nLab > Latest Changes: Hamiltonian mechanics

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2009

    I thought of it and then moved the material on Hamiltonian mechanics from symplectic geometry to its own entry at Hamiltonian mechanics

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeOct 26th 2009

    I added an idea. Note that one can generalise further from symplectic manifolds to Poisson manifolds; John wrote something about this in (I think) an early TWF.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2009

    Yes, and in fact much of the most interesting developments in the Weinstein program comes from the aim to generalize geometric quantization to the case of just Poisson manifolds. All eventually to be discussed..

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeOct 28th 2009
    • (edited Oct 28th 2009)
    Karasev was developing a similar program independently (with help from Maslov) in a bit more physical language, and a bit earlier (quantization of nonlinear systems in the language of Poisson geometry) and he independently discovered symplectic groupoids. Geometric quantization had the deepest discoveries however in the realm of representation theory (Kirillov, Auslander, Kostant, Vogan...) where the present theory is extremely complicated and subtle and has interesting refinements in quantum group world.

    Much more mathematics can be quantized, not only Poisson geometry.

1 to 4 of 4

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