Amplitude of a process + interference term, how what?

[moss]

Hello guys,

Suppose a process 1+2--->3+4 proceeds thru 3 different intermediate particles and has 3 Feynman diagrams. When we compute the probability then what does the cross terms( interference ) mean? and do we have to always compute the cross terms?

What I mean is that when you have 3 Feynman diags for a process then, you add the amplitudes and then absolute square? or you absolute square and then add? why and why not?

Suppose also that the coupling constants are all different in the 3 Feynman diagrams.

Can anybody tell me that are there any conditions when you don't consider those cross terms or interference terms?
If you know of any text or article where I can read about this then help me out.
THX.

 

[mfb]

When we compute the probability then what does the cross terms( interference ) mean?

The same as interference in a double-slit. In quantum mechanics we have to add amplitudes, not probabilities. Why? Well, it is an experimental result. Otherwise we would not need quantum mechanic, but classical mechanics (where you add probabilities) gives the wrong result.

and do we have to always compute the cross terms?

Directly or indirectly, yes, as they influence the probability.

 

[moss]

The same as interference in a double-slit. In quantum mechanics we have to add amplitudes, not probabilities. Why? Well, it is an experimental result. Otherwise we would not need quantum mechanic, but classical mechanics (where you add probabilities) gives the wrong result.Directly or indirectly, yes, as they influence the probability.

You mean that e.g the chiral electron+positron -->muon+anti-muon one has to sum the amplitudes of all the polarized out-coming muon and then compute probability? what about first computing the probability and then adding them? My qs. is based on Peskin & Schroeder 5.22 till 5.24.
This is confusing me really, help me a bit more. THX.

 

[mfb]

All processes that lead to the same final state have to be added with their amplitudes.
For different final states (e.g. different polarizations) you don't add amplitudes of course. That's like adding amplitudes of electron/positron and muon/antimuon production: how would that make sense?

 

[moss]

All processes that lead to the same final state have to be added with their amplitudes.
For different final states (e.g. different polarizations) you don't add amplitudes of course. That's like adding amplitudes of electron/positron and muon/antimuon production: how would that make sense?

Please confirm; For the same final state we add amplitude and then compute probability, even if the final state is reached thru different Feynman diags. with different coupling constants. For different final states (helicity staes) we compute probability separately then add ...Right??

 

[torquil]

If you know of any text or article where I can read about this then help me out.

Maybe this could be helpful:
http://www.feynmanlectures.caltech.edu/III_03.html#Ch3-S1

 

[mfb]

Please confirm; For the same final state we add amplitude and then compute probability, even if the final state is reached thru different Feynman diags. with different coupling constants. For different final states (helicity staes) we compute probability separately then add ...Right??

Sure.
This is standard quantum mechanics.

 

[moss]

Sure.
This is standard quantum mechanics.

Thanks mfb...it is about 10 years I did all that and forgot and the funny thing is that link above of Feynman lectures, same thing is collecting dust in my bookshelf.