  Free bosonic fields are investigated at a classical level by imposing their
characteristic de Broglie periodicities as constraints. In analogy with finite
temperature field theory and with extra-dimensional field theories, this
compactification naturally leads to a quantized energy spectrum. As a
consequence of the relation between periodicity and energy arising from the de
Broglie relation, the compactification must be regarded as dynamical and local.
The theory, whose fundamental set-up is presented in this paper, turns out to
be consistent with special relativity and in particular respects causality. The
non trivial classical dynamics of these periodic fields show remarkable
overlaps with ordinary quantum field theory. This can be interpreted as a
generalization of the AdS/CFT correspondence.
