  All quantum field theories that describe interacting bosonic elementary
particles, share the feature that the zeroth order perturbation expansion
describes non-interacting harmonic oscillators. This is explained in the paper.
We then indicate that introducing interactions still leads to classical
theories that can be compared with the quantum theories, but only if we
terminate the expansion somewhere. `Quantum effects' typically occur when some
of the classical variables fluctuate too rapidly to allow a conventional
description, so that these are described exclusively in terms of their energy
eigen modes; these do not commute with the standard classical variables.
Perturbation expansions are not fundamentally required in classical theories,
and this is why classical theories are more precisely defined than the quantum
theories. Since the expansion parameters involve the fundamental constants of
nature, such as the finestructure constant, we suggest that research in these
classical models may lead to new clues concerning the origin of these
constants.
