Classical geometry to quantum behavior correspondence in a Virtual Extra Dimension

TL;DR

This paper explores a classical-geometry approach to quantum behavior using a virtual extra dimension, revealing a duality with extra-dimensional theories and applications to QCD phenomenology.

Contribution

It introduces a geometric framework linking classical boundary conditions with quantum phenomena and demonstrates a duality with extra-dimensional models, inspired by AdS/CFT correspondence.

Findings

Derivation of Feynman path integral from classical cyclic dynamics.

Encoding interaction kinematics via boundary geometrodynamics.

Application to QGP freeze-out model showing AdS/QCD analogies.

Abstract

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.