added pointer to today’s:

- Pritish Sinha, Ankit Yadav,
*Poisson Geometric Formulation of Quantum Mechanics*[arXiv:2312.05615]

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.

]]>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.

]]>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.

]]>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.

]]>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.

]]>added the original reference:

- Tom W. B. Kibble,
*Geometrization of quantum mechanics*, Communications in Mathematical Physics**65**(1979) 189–201 [doi:10.1007/BF01225149]

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

Added also:

- Dorje C. Brody, Lane P. Hughston,
*Geometric Quantum Mechanics*, J. Geom. Phys.**38**(2001) 19-53 [arXiv:quant-ph/9906086, doi:10.1016/S0393-0440(00)00052-8]

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

]]>Added:

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

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

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