Question: What is Virtuality for a Virtual Photon?

[dvoraky]

What is the Virtuality for a virtual photon (Q^2). How's it defined?

What is the virtual photon's frequency then?

Any relations between them?

Thanks.
:!)

 

[marlon]

A particle is virtual when :

1) it's energetics do not respect the Einstein energy relation.
2) it corresponds to internal Feynman lines.

Both 1) and 2) are equivalent and particles that are caracterized thereby are called off mass shell.

One cannot speak about the frequency of a virtual particle because this value is uncertain. Virtual particles arise because in QFT, the conservation of total energy can be violated for a very short time, thanks to the HUP.

Just do a search on this in our forum because we have covered this subject many times before.

regards
marlon

 

[BenLillie]

The technical definition of virtuality is just the amount by which the particle is off it's mass shell. That is, for a photon of 4-momentum Q^{mu} then Q^2, the 4-momentum squared, should be zero since the photon is massless. The amount by which it is not is what we call the virtuality. For a massive particle this would be modified to be "virtuality = Q^2 - m^2", where m is the mass of the particle. Again, it's just the amount by which the particle's 4-momentum is off it's mass shell.

Also, it's not entirely true that one can't talk about the frequency of a virtual photon. If you look at the Feynman expansion the 4-momentum is conserved at every vertex. In a tree-level process, therefore, the 4-momentum of every internal line in a diagram is well defined in terms of the momenta of the incoming and outgoing particles. Take, for example, the deep-inelastic scattering process: e- p -> e- X, where an electron scatters off a proton by exchange of a virtual photon. We can, and do, talk about the 4-momentum (and hence energy) transferred by the photon.

 

[marlon]

Also, it's not entirely true that one can't talk about the frequency of a virtual photon. If you look at the Feynman expansion the 4-momentum is conserved at every vertex. In a tree-level process, therefore, the 4-momentum of every internal line in a diagram is well defined in terms of the momenta of the incoming and outgoing particles. Take, for example, the deep-inelastic scattering process: e- p -> e- X, where an electron scatters off a proton by exchange of a virtual photon. We can, and do, talk about the 4-momentum (and hence energy) transferred by the photon.

Well, this is what i wanted to point out but you are making a conceptual error here. We can only talk about energy transfer between vertex points because in such points, the conservationlaws still hold. But in these points, one is not able to talk about virtual particles. So, there is no direct link between energy and virtual particles because virtual particles only exist in between vertex points. The energy of virtual particles is UNCERTAIN, thus one cannot speak about their energyvalue. The fact that the energy is uncertain is the very foundation for the existence of virtual particles.

regards
marlon