  In the Lorentz invariant formalism of compact space-time dimensions the
assumption of periodic boundary conditions represents a consistent
semi-classical quantization condition for relativistic fields. In
[arXiv:0903.3680] we have shown, for instance, that the ordinary Feynman path
integral is obtained from the interference between the classical paths with
different winding numbers associated with the cyclic dynamics of the field
solutions. By means of the boundary conditions, the kinematics information of
interactions can be encoded on the relativistic geometrodynamics of the
boundary [arXiv:1110.0315]. Furthermore, such a purely four-dimensional theory
is manifestly dual to an extra-dimensional field theory. The resulting
correspondence between extra-dimensional geometrodynamics and ordinary quantum
behavior can be interpreted in terms of AdS/CFT correspondence. By applying
this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain
fundamental analogies with basic aspects of AdS/QCD phenomenology.
