When is a propagator on shell?

[nolanp2]

Hey all,

just a simple question that's confusing me about amplitudes for feynman diagrams. How do i know whether a system needs to be considered as being on shell, and hence has an imaginary component included in the denominator of the propagator?

If i have one propagator which is required to be on shell, does that mean all propagators in the diagram must now be on shell?

thanks

 

[RedX]

heh I'm not sure. I do know that after a Wick rotation you ought to be able to neglect the imaginary component in the demoninator I think. maybe there are cases where even with a Wick rotation you can't neglect it. no wait after you take care of the demoninator with Feynman parameterization then after Wick rotation you should be able to ignore the imaginary part of the denominator.

 

[Entropia]

A propagator is considered to be on shell when it satisfies the mass-energy relationship of the particle it represents. In other words, the energy and momentum of the particle must be equal to its mass, as dictated by the relativistic dispersion relation. This is necessary for the propagator to accurately describe the behavior of the particle in the given system.

Whether or not a system needs to be considered on shell depends on the specific context and the desired level of precision. In some cases, off-shell contributions may be negligible and can be ignored, while in others they may be crucial for the calculation.

If one propagator in a Feynman diagram is required to be on shell, it does not necessarily mean that all propagators in the diagram must also be on shell. Each propagator should be treated independently and considered in the context of the specific system being studied.

It is important to carefully consider which propagators need to be on shell in order to accurately describe the system, as including unnecessary on-shell conditions can complicate the calculation without adding any significant improvement to the result. Ultimately, the decision of whether or not to include an on-shell condition for a propagator should be based on the physical significance and relevance to the system being studied.