As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modeled.
In this sense, virtual particles are an artefact of perturbation theory, and do not appear in a nonperturbative treatment.
As such, their objective existence as "particles" is questionable;[citation needed] however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms.[citation needed]