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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.

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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.

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  • $\begingroup$ 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? $\endgroup$ – Saladino Mar 13 '17 at 15:05
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    $\begingroup$ @Saladino because a virtual particle is an iconic line carrying all the quantum numbers of its name except the mass , and the mass appears in the denominator of the propagator, so the handwaving identification to "particle" is tempting. Virtual loops of particles antiparticles that exist in calculations of higher order diagrams, extending the delta(e)delta(t) of the Heisenberg uncertainty principle lead to this handwaveing popularization of these loops existing in a limited time. . Connected to a real particle with energy and momentum a delta(E) can be envisaged , not in the vacuum though. $\endgroup$ – anna v Mar 13 '17 at 15:22
  • $\begingroup$ Ah yes @annav thanks, I could have not put it better! $\endgroup$ – AccidentalFourierTransform Mar 13 '17 at 15:28
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    $\begingroup$ @Saladino: physicsforums.com/insights/vacuum-fluctuation-myth for how the myth about the life of virtual particles was born. $\endgroup$ – Arnold Neumaier Dec 31 '17 at 13:01

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