# Virtual particles creation operator

In QFT when we consider an external leg we use the creation operator to specific the state of a particle. So this is created onshell with this creation operator. But for virtual particles, those that exist for a limited time and are offshell, how can I create those? I ask this because I found that when talking about the Casimir effect people relate quantum fluctuations to the creation of virtual particles.

Virtual particles do not exist for a limited time, they are not off-shell states, and you cannot create those. They are Wick contractions of fields in the interaction picture, in the Dyson expansion of the $S$ operator. They are not particles, and they behave nothing like a particle.
• Ok, I understand that they are Wick contractions. But why some people when they speak about the Casimir effect the talk about particles that exist for a little time $\Delta t$ given by the indetermination principle? Also here en.wikipedia.org/wiki/Virtual_particle it's written "In physics, a virtual particle is a transient fluctuation that exhibits many of the characteristics of an ordinary particle, but that exists for a limited time." How did this analogy pop out? – Saladino Mar 13 '17 at 15:05