In srednicki , page 37 . In derivation of LSZ reduction formula , he introduces the time-order operator , so no time-dependent creation/annihilation operators are left in the transition amplitude . How can this be justified mathematically ? And if I understand this correctly If time ordering is not used, then a term like $< 0\mid a_{1}\left ( -\infty \right )a_{2}\left ( -\infty \right )a_{1^{\tilde{}}}^{\dagger}\left ( \infty \right )a_{2^{\tilde{}}}^{\dagger}\left ( \infty \right )\mid 0> $ this mean that there's a contribution that depend on the amplitude of transition from the final momenta to the initial momenta but quantum mechanically the final momenta are not known in advance so such a term can't contribute to the process .Does this explain the use of time-ordering physically?
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