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Does the exist any mathematical formalism (model) describing the behavior of light and incorporating its particle character (divisibility, quantization) and wave character? (i.e. quantized wave model)

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It's called "quantum field theory". –  LuboŇ° Motl Jul 19 at 16:14
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In particular for photons it's quantum electrodynamics. –  Pu Zhang Jul 19 at 22:33

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