Surprisingly common objection when doing something new: but I can already solve the problems I can already solve. Excellent response by Rotapic.twitter.com/5P7fPMWFFK
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It's all about the link between symmetries and conserved quantities. Coadjoint orbits, and not cotangent bundles, are the things to ponder.
A phase space should have exactly the structure needed to ensure that each symmetry correspond to a conserved quantity. That's the key idea.
Twitter isn't a great format for how you are commenting. You could write this up in a blog entry and put a link to it in a Twitter response.
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