Suppose I want to bypass the entire Hamiltonian formulation of quantum field theory and define the theory using a path integral. Thus all I can calculate are Green's function which are time ordered products of local operators. Given only these (no expansions of the field in creation anihilation operators etc.), how can I show that the fields and local operators commute at space-like separation? [\phi(x),\phi(y)]=0, when x,y are spacelike separated?(adsbygoogle = window.adsbygoogle || []).push({});

KH

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# Time ordered product vs. commutator in path integral

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