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 Sci Advisor Thanks P: 2,502 I don't understand this remark. Of course an creation operator wrt. the energy-momentum eigenstates adds an onshell (asymptotically) free particle with the given momentum (and spin or helicity) to the state the creation operator adds on. In terms of Feynman diagrams, which are nothing else than a special notation for the calculation of S-matrix elements in perturbation theory, these initial- or final-state asymptotically free particles are represented by the external legs. The "virtual particles" are represented by inner lines, connecting to vertices of the diagram. These lines stand for particle propagators. At each vertex, energy-momentum conservation holds, and usually the four momenta of internal lines are off-shell. It's in fact a problem in naive perturbation theory, when the kinematics of a process is such that an internal line's four momentum becomes on-shell since there the propagator has a pole. The reason are usually infrared of collinear divergences when massless particles are involved. These divergences have to be remedied by an appropriate resummation of many diagrams (e.g., by the Bloch-Nordsieck argument in QED).