A formulation of field theory given by Van Hove in 1955 is shown to be useful for putting parton-model-like ideas'' on firm theoretical grounds. This is done by discussing electron-proton deep-inelastic scattering, electron- positron annihilation, and the proton elastic form factor. A basic requirement that must be imposed on any field theory in order to discuss the concept of hadronic constituents is given. To put the formulation on a firm ground (with respect to renormalizability), we assume that the wave-function renormalization constants of the theory are finite. This assumption satisfies the above- mentioned basic requirements, though it probably is not necessary. Within this framework we prove that nu W2(q2, nu ) is the same as that derived in the parton model. In this formalism, electron-positron annihilation is quite different in character from deep-inelastic electron-proton scattering. The constancy of the ratio sigma (e+e yields hadrons)/ sigma (e+e → mu + mm) can be derived only if much stronger assumptions than the one mentioned above are adopted.The price paid for simplicity in the renormalization procedure is two physically undesirable results: (a) The proton elastic form factor is probably finite at large momentum transfer. and (b) nu W2 is finite and nonzero atmore » x=1. It is conjectured that these problems can be solved without changing other results by allowing wave-function renormalization constants to become infinite.« less