Thanks! I explain everything in more detail in my paper than in this summary based on the introduction. So, I hope it makes more sense. If not, please ask questions. Like every author of every paper, I’m dying for questions from people who have actually looked at it.

]]>Interesting! I was tempted to generalize beyond Banach Lie groups, because classical mechanics as I described it doesn’t easily fit in that framework: the relevant group is the group of Poisson diffeomorphisms of a Poisson manifold, and that’s some more general sort of infinite-dimensional Lie group (unless one uses other tricks, which bring along their own technicalities). But I decided that the essential points of the paper would be buried if I sank any deeper into questions like “what’s the best category of infinite-dimensional Lie groups?”

]]>I should have added: the assignment is also postulated to be smooth for a regular Lie group, so this is rather strong!

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