Perusing Terry Tao's notes on harmonic analysis in the phase plane, I came across this statement:
"Roughly speaking, symplectic geometry is to harmonic analysis (and representation theory) as classical mechanics is to quantum mechanics, but a deeper pursuit of this connection is beyond the scope of this course."
Can anyone elaborate on this statement? Thanks :)
Just to make sure I get a sophisticated answer, but also one that's not over my head, I should mention that I've studied a fair amount of harmonic analysis, and I've done a bit of class. and quantum mech. I haven't done any symplectic geometry outside of studying class. mech.