  In 1952, L\'{e}on van Hove published an article, in French, with the title
``Les difficult\'{e}s de divergences pour um mod\`{e}le particulier de champ
quantifi\'{e}''. The article is frequently cited in relation to Haag's theorem
and to the issue of the existence of unitarily inequivalent representations of
the canonical commutation relations in Quantum Field Theory. Summarizing in
brief, it suggests a link between the appearance of divergences in perturbative
Quantum Field Theory and the fact that quantum states belonging to an
interacting theory do not belong to the same Hilbert space of the free theory.
It also suggests that renormalization fails to provide an accurate description
of the time evolution of the quantum field, although it correctly accounts for
the S matrix. Due to its relevance, and to the difficulty of finding an English
translation, the ideas contained in this article are proposed again here,
expanded with derivations and accompanied by a discussion aimed at putting the
analysis into context. We highlight the main points from the perspective of a
contemporary reader, and underline the differences with the standard approach
usually taught in curricular courses in Quantum Field Theory.
