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This is very common to show up in books. Here's one example from Thomson's Modern Particle Physics. When talking about the general expression for the $a \rightarrow 1+2$ relativistic decay $$\Gamma_{fi}=\frac{p^*}{32\pi^2m^2_a}\int|M_{fi}|^2d\Omega$$ he says that the fundamental physics is contained in the (Lorentz invariant) matrix element. What does this mean?

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    $\begingroup$ He means that's the important part. Everything else in that equation is a bunch of annoying kinematic factors, which don't depend on the actual nature of the interaction. $\endgroup$
    – knzhou
    Jul 29, 2016 at 2:01
  • $\begingroup$ I'm voting to close this question as off-topic because it is a question about communication (or mis-communication). It asks what a particular author is trying to convey by a popular phrase. Answering does not require the application of physics, only the conventions of science communication. $\endgroup$ Jul 29, 2016 at 16:57

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Fundamental physics , as the comment by knzhou says, is the mathematical formulation for the interaction.

The matrix element contains the wavefunctions and the potential that gave rise to the interaction under study. This is for simple transitions, but the logic is the same even for the complicated standard model of particle physics with all the three interactions.

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