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nLab > Latest Changes: geometrical formulation of quantum mechanics

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2023

    a minimum of an Idea-section, but mainly to record some references

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 1st 2023

    Added:

    • L. P. Hughston, Geometry of stochastic state vector reduction, 452:1947 (1996), doi.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2023

    Thanks. I added journal name and jstor-link (here)

    Added also:

    and will try to finally add now the original articles by Kibble…

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2023

    added the original reference:

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2023

    Incidentally I think this topic should really be called “symplectic formulation…”.

    It’s weird that all authors insist on the vague “geometric”. (Also the Heisenberg picture is “geometric” in the end, even if NC geometric.)

    So on absolute grounds the entry might deserve renaming, but it would probably be unhelpful to the search engines, so I am hesitant.

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 1st 2023

    Re #5: “Symplectic formulation of quantum mechanics” is potentially ambiguous, since it could be interpreted as referring to the geometric quantization picture of quantum mechanics.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 2nd 2023

    That potential confusion with “geometric quantization” is certainly only made worse by saying “geometric quantum mechanics”.

    On the other hand, the term “symplectic mechanics” is standard, as shorthand for “symplectic formulation of classical mechanics as about Hamiltonian flows”. With this in mind, “symplectic quantum mechanics” would exactly express what’s going in.

    And then one could transparently ask:

    “Why, conceptually, does geometric quantization of symplectic classical mechanics yield symplectic quantum mechanics?”

    which is, I think, the most interesting question that a symplectic geometer wants to ask here, now viewining, with Kibble and followers, quantization as a process that takes one symplectic manifold to (not a deformation of symplectic geometry but) another symplectic manifold.

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 2nd 2023

    I would say it is unlikely that the nLab can unilaterally enact a change in terminology for this specific subject, which probably makes it prudent to stick to the existing terminology.

    I see numerous papers using the word “geometric” and similar derived words, but none that use “symplectic quantum mechanics”. This is the case for the references in the 2015 paper by Heydari, for example

    It is my perception that the title of the article is often taken to be (by the readers) as the most common choice of terminology, which in this case would inevitably lead to confusion when trying to search for papers.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2023

    Yes, that’s why I said in #5 I am hesitant.

    But it’s dangerous to keep sacrificing what is right for what is mainstream.

1 to 9 of 9

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