“The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.”
Taken from David Tong’s page at Cambridge (see here).
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Yes, so now we have to move beyond the categorification/decategorification version to something more abstract …
Indeed, we are waiting for something new to happen…
It’s true and it’s sad. Standard physics relies on linear approximations rather than non linearity; this is especially true in the foundations of elementary particles.
Wish me and Kea luck, we’ve a paper under peer review at PRD. It gives a parameterization of 3×3 unitary matrices which is not based on the discrete Fourier transform instead of the usual product of 1-parameter groups (which amounts to a linearization of the problem of understanding the group).
Alas, the rejection email shows no sign of any referee reports. Apparently we never deserve constructive criticism – only outright rejection.