Particles and waves are just different basis functions. The best ones for physics are probably yet to be discovered.
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Particles are not basis functions. They are irreducible representations of the Poincaré group.
They're both. Irreps can be used as basis functions, and they are in QFT.
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So what's a basis function? Like a Hermite polynomial? Wouldn't you expand a wave function in basis functions? I realize you know what you're talking about, but saying particles are basis functions confuses me.
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Any set of functions that you express a function of interest as a combination of. (Linear, in the standard case, but possibly nonlinear, e.g., deep networks.)
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