Interactions such as scattering between real particles and in drawing certain Feynman diagrams. Do virtual particles have any real existence in vacuum when there are no real quanta of the fields present?
No, because they are not real under any circumstances.
I think, inexperienced though I am, that somebody needs to attempt to answer this valid question. I used to think VP's were real on Tuesdays, Thursdays and Saturday and not real on the other days of the week.
Virtual particles are not real, they are book keeping mathematical entities, that allow calculations to be made for say, scattering amplitudes between two electrons, as one example.
Another way to describe them, and I apologize if this not news to you, is to use the term on and off shell, instead of virtual particles.
Wikipedia On and Off Shell
In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell.
In quantum field theory, virtual particles are termed off shell (mass-shell in this case) because they don't satisfy the Einstein energy-momentum relationship; real exchange particles do satisfy this relation and are termed on shell (mass-shell). In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on shell equations. Noether's theorem is also another on shell theorem.
Off shell particles are invoked to deal with calculations in somewhat the same way as electrical engineers use the square root of minus one, when calculations involving their work are needed. $\sqrt -1$ is used as an intermediate math step, but as long as they end up with real current and voltage values, the electrical guys are OK with that.
A real photon exists when you shine a light on a metal plate to eject some electrons, every aspect of that experiment is measurable and the photon will last until it's absorbed by an atom.
This last paragraph is my own personal view, and different people have different interpretations on what reality is. If you start chopping up a stick of wood, as you know, you eventually will not end up with tiny, tiny pieces of wood, you will end up with elementary particles, which can only be described by math.
Rembering that if it walks like a duck, and it quacks like a duck.....if an elementary particle, say an electron, even if you call it an excitation of a field, as in QED, follows mathematical rules and is explainable only in math terms, then it is, in my totally naive worldview, a mathematical object, similar to a virtual particle but different in that we take it as real because it follows on shell, not off shell rules.
Please read Matt Strassler's blog on this virtual particle idea, the silly notions in the above paragraph are a personal viewpoint, that are certainly not original to me. I think we can go back to Plato for the same general idea, but he couldn't prove his hypothesis and neither can I.
