# I 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 Feynmann 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.

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#### jtbell

Mentor
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 $P(\vec x) = |\psi(\vec x)|^2 = \psi^*(\vec x)\psi(\vec x)$.

• Natchanon

Staff Emeritus
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,

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#### 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 Schrodinger 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.

• Natchanon

"What exactly is the amplitude of an interaction?"

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