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Sep 21, 2022 at 7:58 comment added Vivek In same way can I think that integration $$\int dp_0 \delta(p_0 -E)$$ where we are performing the $p_0$ integration respects the mass shell condition.
Sep 19, 2022 at 22:50 comment added AfterShave Yes, think of the delta functions like probability distributions that are infinitely peaked at values which respect conservation laws.
Sep 19, 2022 at 9:24 comment added Vivek So without assuming that energy and momentum are conserved (p_i = p_f), elements of scattering matrix has to be integrated over complete phase space and so that final answer respects the energy and momentum conservation. thanks
Sep 19, 2022 at 8:57 history answered AfterShave CC BY-SA 4.0