Since the paper is rather long I'll try to summarize a little the idea which is a consequence of the fact that Time can be defined only assuming periodicity or vice versa.
The action of a free scalar field defined in a time interval T allows
periodic solutions with periodicity T. The frequency of the free periodic fields fixes the energy of the quanta as usual.
The periodicity introduces a non-locality in
the theory which however has no hidden variables. Similarly to the KK theory
where there is a quantization of the mass spectrum, here there is a
quantization of the energy spectrum which depends on the inverse of the
period through the Planck constant. The dispersion relation of the
quantized spectrum is the correct one also for massive scalar fields
since the proper time acts like a "virtual extra dimension". This
implies that the periodicity varies with the energy through Lorentz
transformations or interactions so that special relativity and
causality hold.
Periodic fields are stationary waves and they trivially give rise to
Hilbert space.
the Schrodinger equation follows as the "square root" of the KG equation and in the
Hilbert space the time evolution operator is Markovian. From these
results already contained in the theory, it is immediate to derive the Feynman path integral, which is interpreted as a sum over all the periodic paths, as well as
Commutation relations and Uncertainty relations. These important links
to QM are derived in par.2 and par.3 which are the core of the paper.
As a consequence of the quantization of the energy spectrum the massless periodic fields avoid the UV catastrophe of the black body radiation whereas the
non-relativistic free particle and the double slit experiment emerge as
a consequence of the fact that in the non relativistic limit only the
first harmonic of the energy spectrum is relevant. The Quantum Harmonic
Oscillator is exactly solved due to the analogy with the
Bohr-Sommerfeld condition. An attempt to solve the interaction case
is done by describing periodic fields in a AdS metric, the result is similar to the AdS/CFT correspondence. In fact, as classical fields with periodic BCs in Minkowski metric should correspond to quantized free fields, periodic fields in a deformed metric should describe the quantization of interacting fields. The AdS/QCD correspondence comes from the fact that in the Bjorken model for quark-gluon plasma this deformation is exponential, giving a virtual warped metric.
