Transition Amplitude

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Transition Amplitude in Free Field Theory
The previous person shows an example with a two particle to one, what would happen if we were to get more particles out, like 3 or 4? Can you still call the state $a^{dagger} _{k _{out}}$ for the out particles or would one need to have three/four ect individual out states to manipulate?

tbt · Answer

The out state would be $langle k_1^f ldots k_n^f |= langle 0 | a^dagger_{k_1}ldots a_ {k_n}^dagger$, with $n$ number of particles in the final state.
You can convince yourself (invoking an argument like in the question you reference) that, in that context, inner products between states with different numbers of particle are zero.

Transition Amplitude

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