Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory

In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In this paper we summarise some of the major achievements, rigorously proven also in several recent peer-reviewed papers, of this innovative formulation of quantum particle physics.Comment: 35 page

Gauge Interaction as Periodicity Modulation

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [arXiv:0903.3680]. 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.Comment: 37 pages, 2 figures. Version published in Annals of Physics (2012). New title, comments and minor correction

Elementary spacetime cycles

Every system in physics is described in terms of interacting elementary particles characterized by modulated spacetime recurrences. These intrinsic periodicities, implicit in undulatory mechanics, imply that every free particle is a reference clock linking time to the particle's mass, and every system is formalizable by means of modulated elementary spacetime cycles. We propose a novel consistent relativistic formalism based on intrinsically cyclic spacetime dimensions, encoding the quantum recurrences of elementary particles into spacetime geometrodynamics. The advantage of the resulting theory is a formal derivation of quantum behaviors from relativistic mechanics, in which the constraint of intrinsic periodicity turns out to quantize the elementary particles; as well as a geometrodynamical description of gauge interaction which, similarly to gravity, turns out to be represented by relativistic modulations of the internal clocks of the elementary particles. The characteristic classical to quantum correspondence of the theory brings novel conceptual and formal elements to address fundamental open questions of modern physics.Comment: 6 pages. Accepted for publication in Europhysics Letters (EPL) 30 April 201

Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity

One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation {\it geodesically complete}, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability.Comment: 38 pages, 6 figures. V2: Added: a word to the title, clarifications, an appendix, many references. To appear in JCA

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 [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.Comment: 60 pages. Version published in Annals of Physics (2012). Minor correction