What exactly is the amplitude of an interaction?

[Natchanon]

I've been reading Griffths' intro to elementary particles and I encountered this symbol that looks similar to "M" called amplitude, which can be calculated by analyzing the Feynman diagram of an interaction. What exactly is it? When I hear amplitude I imagine waves, but not sure what this one's supposed to mean.

 

[jtbell]

This is the "probability amplitude". You multiply it by its complex conjugate in order to get a type of probability density for the interaction, similarly to the way in ordinary QM the position probability density $P(\vec x) = |\psi(\vec x)|^2 = \psi^*(\vec x)\psi(\vec x)$.

 

[Vanadium 50]

If you have not seen a quantum mechanical amplitude, it is likely that Griffiths is too advanced for you at the moment. I would suggest backing off to a book on QM, and when you have that down, return to Griffiths,

 

[Natchanon]

If you have not seen a quantum mechanical amplitude, it is likely that Griffiths is to advanced for you at the moment. I would suggest backing off to a book on QM, and when you have that down, return to Griffiths,

I have read his book intro to quantum mechanics and have taken an intro to QM class. I know about Schrödinger eq and how to calculate probability from it.

 

[Natchanon]

This is the "probability amplitude". You multiply it by its complex conjugate in order to get a type of probability density for the interaction, similarly to the way in ordinary QM the position probability density $P(\vec x) = |\psi(\vec x)|^2 = \psi^*(\vec x)\psi(\vec x)$.

So intergral of|M|^2 is the prob that particular interaction will occur?

 

[Mr rabbit]

So intergral of|M|^2 is the prob that particular interaction will occur?

Not quite. In particle physics there are two kind of processes: scattering and decays. There are two famous observables that you can calculate with QFT: cross section for the first and decay width for the second.

For both you need $| \mathcal M | ^ 2$, but also some kinematics of the process.

$\mathcal M$ represents somehow the probability, but it is not as direct as in QM.