Classical geometry to quantum behavior correspondence in a virtual extra dimension

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 Dolce (2011) [18] 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 kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. 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.

► Quantum behavior is related to the intrinsic periodicity of isolated systems.
► A periodic phenomenon can be parameterized by a virtual extra dimension.
► KK modes are used to describe the quantum excitations.
► 5D classical geometry encodes 4D quantum behavior.
► Geometrodynamical description of AdS/QCD as modulation of space–time periodicity.