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 foundamental 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.

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [1]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore, gauge interaction is described as invariance of the theory under local deformations of the boundary, the resulting local variations of field solution are interpreted as internal transformations, and the internal symmetries of the gauge theory turn out to be related to corresponding local space-time symmetries. In the case of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED. IntroductionIn 1918 Weyl [2] introduced the idea of gauge invariance in field theory in an attempt to describe electromagnetic interaction as invariance under local transformations of space-time coordinates. In particular he tried to extend the principle of relativity of the choice of reference frame to the choice of local units of length. For this reason the idea was named gauge invariance. The requirement of gauge invariance in fact necessitates the introduction of a new field in the theory, named compensating field [3]. It cancels all the unwanted effects of the local transformations of variables such as the related internal transformation of the matter fields, and enable the existence of a local symmetry. Weyl noticed that such a compensating field has important analogies with the electromagnetic potential. His proposal was very appealing because of its deep analogies with the geometrodynamical 1 description of General Relativity (GR). EvenEmail address: ddolce@unimleb.edu.au (Donatello Dolce) 1 The term "geometrodynamics" is used as a synonym to indicate a geometrical description of interactions [4]

In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semiclassical quantization condition for relativistic fields. In [1] 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 [2]. 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. IntroductionOriginally proposed by T. Kaluza [3] and O. Klein [4], field theory in compact eXtra Dimension (XD) represents one of the most investigated candidates for new physics beyond the Standard Model (SM), providing an elegant explanation for the hierarchy problem [5,6,7,8].

We discuss the fermion couplings in a four dimensional SU(2) linear moose model by allowing for direct couplings between the left-handed fermions on the boundary and the gauge fields in the internal sites. This is realized by means of a product of non linear $\sigma$-model scalar fields which, in the continuum limit, is equivalent to a Wilson line. The effect of these new non local couplings is a contribution to the $\epsilon_3$ parameter which can be of opposite sign with respect to the one coming from the gauge fields along the string. Therefore, with some fine tuning, it is possible to satisfy the constraints from the electroweak data.Comment: Latex file, 20 pages, 4 eps figure