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center o bass

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$$\square G(x,x') = \delta^{(4)}(x-x')$$

where ##\square= \partial_\nu \partial^\nu## is the wave operator and ##x,x'## are four vectors labeling events in spacetime. If we require ##G(x,x') \to 0## as ##x \to \infty## it is often stated that ##G(x,x')## must depend only on the relative distance due to the symmetry of the problem. But I wonder, how can one prove this rigorously?