Figure 1: Topological vacuum bubble.

Feynman diagrams for interference involving a real particle and a virtual particle–hole excitation from vacuum. Full (empty) circles represent particles (holes). Solid (dashed) lines denote propagations of real (virtual) particles. (a) Diagram for the interference of two processes: (a₁, blue) A real particle propagates, a virtual particle–hole pair is excited, then the pair self-annihilates after the virtual particle winds around the real one. (a₂, magenta) A real particle propagates. The entire virtual process constitutes a vacuum bubble. For anyons, the bubble gains a topological braiding phase 2πν from the winding. (b) Partner diagram of a. Here a virtual particle, constituting another bubble, does not encircle a real one and hence gains no braiding phase. The diagrams in a and b contribute to observables for anyons, while they do not for bosons and fermions.