Take a [tex]\lambda \phi^4[/tex] theory. To first order in λ, the 2x2 scattering amplitude is:(adsbygoogle = window.adsbygoogle || []).push({});

iM=-iλ

So the amplitude <f|S|i> is then <f|(1+iM)|i>=<f|i>+iM<f|i>.

Letting f=i, the probability is greater than 1! It is equal to the norm |1+iM| which is sqrt[1^2+λ^2].

How is it that two particles in the state |i> have a probability greater than 1 of being in the same state |i> after scattering?

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# S-matrix unitary?

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