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From my understanding, virtual particles are actually "disturbances" between two elementary particle interactions and appear during cross sections of these interactions. What equation(s) describe this process? Is there a linear relationship?

For example, take the Casimir effect when two mirrors are aimed at each other. Since these virtual photons have the potential to become real particles, is there some sort of linear relationship that shows how these virtual photons become "disturbed" enough to develop into real photons? What is the equation that demonstrates this?

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    $\begingroup$ Virtual means not obeying energy mass relation. Nothing magical about it, just math. $\endgroup$
    – Asphir Dom
    Jul 29, 2015 at 13:37

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"A rapidly moving mirror that turns virtual photons into real ones is the first experimental evidence of the dynamical Casimir effect."

http://www.technologyreview.com/view/424111/first-observation-of-the-dynamical-casimir-effect/

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  • $\begingroup$ This is indeed helpful, but I am hoping to find out the relationship. Can it be explained through an equation? I will also clarify my question since I could be more clear. $\endgroup$
    – crockpotveggies
    Mar 24, 2015 at 3:04
  • $\begingroup$ And by the way thanks for answering! You've been very helpful $\endgroup$
    – crockpotveggies
    Mar 24, 2015 at 3:07
  • $\begingroup$ Followed the material from your answer, and did some Googling. Am I correct in assuming that I can derive this relationship using the Dirac Equation? $\left(\beta mc^2 + c(\alpha_1 p_1 + \alpha_2 p_2 + \alpha_3 p_3)\right) \psi (x,t) = i \hbar \frac{\partial\psi(x,t) }{\partial t} $ $\endgroup$
    – crockpotveggies
    Mar 24, 2015 at 3:29
  • $\begingroup$ Most likely the virtual particles are embedded in the vertex of some field theory Feynman diagram. I think this was the interpretation explained to me about the vertices. EDIT: I think this a good source: arxiv.org/abs/hep-th/0503158 $\endgroup$
    – John M
    Apr 5, 2015 at 18:26

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