I'd ask this in a physics gen if we had one but alas this board is too full of opinionated schizos to sustain one so I apologize for sloppiness. Consider L^2 or a sufficiently well behaved subspace thereof. The Fourier transform can be expressed as a linear, unitary operator in this space: [eqn] \psi(x) = \hat{\mathcal{F}} \phi(x) = \int_{-\infty}^{\infty} \frac{\exp(-ikx)}{\sqrt{2\pi}}\phi(k) dk [/eqn] [math]\hat{\mathcal{F}}^4 = 1 [/math] makes its powers isomorphic to the cyclic group [math]…