If virtual particles don’t exist, how do laws govern them?

Question

What exactly is the object described in a theory with virtual particles? I feel like they should behave according to laws (they seem to be useful, after all), but if they don’t exist, I can’t see how some law could govern them to the exclusion of any other law. Does something exist which the virtual particles describe?

Answer 1

Virtual particles are just the objects that occupy the interior of Feynman diagrams. Since Feynman diagrams can have infinite loop corrections applied to them, there is no one "true" interior to such diagrams, but rather we must consider the superposition of states between all possible diagrams (assigning weight by the probability of each).

Simply put, virtual particles shouldn't be imagined as being "like" real particles, but they must still obey rules like charge conservation so the exterior parts of the Feynman diagram remain consistent.

For more information on the infinite set of Feynman diagrams for any given interaction, I'll reference you to this question.

Answer 2

Their answer was no, and is now yes. In QFT, and initial state transitions to a final state. One must sum over intermediate states…aka virtual states.

In old-fashioned perturbation theory, it was hard. The states were time ordered and violated energy conservation, but didn’t last long enough to violate Heisenberg's uncertainty principle. This old way of thinking is still used in much educational content, and mostly just confuses laymen.

In 1948, modern QED was developed. Here, the intermediate states are calculated perturbatively a can be drawn as particle lines in momentum space. Energy, momentum, angular momentum, charge, etc are all conserved at the vertices.

Knowledge of basic kinematics should convince you that such a virtual photon in annihilation or scattering does not have zero mass squared. It’s just an approximation to an intermediate field configuration.

That they aren’t real particle is important to remember; however, in Rosenbluth separation and polarized deep in elastic scattering, it’s very convenient to treat them as particles