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One can formulate the quantum theory taking as the starting point the cone of states. The probabilities can be derived from the first principles in this approach. The formulation in terms of states is useful, in particular, in statistical physics. It leads to the notion of inclusive scattering matrix related to inclusive cross-sections. This notion can be applied to the scattering of quasiparticles, where the usual notion of scattering matrix does not make sense.
Maxim Kontsevich