Re: How real are the "Virtual" partticles?

From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 03/11/05 

Date: Fri, 11 Mar 2005 08:28:06 +0000 (UTC)

Franz Heymann wrote:
> "Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in message
> news:422AC49F.3030502@univie.ac.at...
>
>>Franz Heymann wrote:
>>
>>>>Unstable particles are modelled exactly like stable particles,
>>>>namely as external lines in a Feynman diagram.
>>>>Virtual particles in Feynman diagrams are exactly those
>>>>which are not given by external lines.
>>>>
>>>>Hence what is real and what is virtual is not affected by a
>>>>diagram rotation - this only affects what is input oand what is
>>>
>>>output.
>>>
>>>I am not happy with that.
>>>Let me illustrate my unhappiness with a specific example.
>>>Take the resonant elastic scattering case:
>>>
>>>pi + p --> Z --> pi + p
>>>
>>>I hope we both agree that the Z is produced as a real but unstable
>>>particle in the s-channel.
>>
>>No. Z is a virtual particle since it is an intermediate line.
>
> You are doing nothing to alleviate my unhappiness.
> If the Z were a virtual prticle, it would not be on its mass shell and
> a mass measurement would not be possible by studying the reaction.

It is not on its (complex) mass shell when it is in an internal line as
in your diagram.

When measured, one has instead a diagram where the Z is detected,
and hence on an external line of Feynman diagrams associated to
the coresponding cross section!

In ordinary scattering experiemnts the existence of the Z shows in
resonances of the cross section. This is evidence for the presence
of the Z in the action, and can be used to calculate properties of Z,
but it is Not a measurement of Z as a particle.

> My undertanding is that the line corresponding to the Z is the
> trajectory of a real Z travelling from its birth to its decay.

This interpretation of Feynman diagrams is popular but completely
unfounded, and gives misleading conclusions if carried beyond the
most superficial view.

> But it is observed, and its (complex) mass is actually measured.

It is _not_ observed in an experiment where the Feynman diagram
you drew is part of the calculation.

It _can_ be observed, but only in a process analyzed with
Feynman diagrams where the Z is an external line.

>>One can also see it by computing
>>the momentum balance and check that the momentum does not lie
>>on the Z's (complex) mass shell, as would be needed for a real Z.
>
> Oh? Sorry, but the Z is no less real than the pi0.
> If the pi0 can decay into two photons, then it can also be created
> bytwo photons.

For the pi0 the situation is the same. If measured, the cross
section for pi0 production or decay comes from an analysis with
external pi0 lines, while in other processes it is a virtual
particle without objective meaning.

Arnold Neumaier

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