Gravity in presence of fermions as a SU(2) gauge theory

The Hamiltonian formulation of the Holst action in presence of a massless fermion field with a non-minimal Lagrangian is performed without any restriction on the local Lorentz frame. It is outlined that the phase space structure does not resemble that one of a background independent Lorentz gauge theory, as some additional constraints are present. Proper phase space coordinates are introduced, such that SU(2) connections can be defined and the vanishing of conjugate momenta to boost variables is predicted. Finally, it is demonstrated that for a particular value of the non-minimal parameter the kinematics coincides with that one of a background independent SU(2) gauge theory and the Immirzi parameter becomes the coupling constant of such an interaction between fermions and the gravitational field.Comment: 5 pages, accepted for publication in Phys. Rev.

Non Abelian gauge symmetries induced by the unobservability of extra-dimensions in a Kaluza-Klein approach

In this work we deal with the extension of the Kaluza-Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce fields equations and gauge transformations in the four-dimensional picture. More precisely, in fields equations any dependence on extra-coordinates is canceled out by an integration, as consequence of the unobservability of extra-dimensions. Thus, by virtue of this extra-dimensions unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein-Yang-Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang-Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.Comment: 5 pages, no figures, to appear in Mod. Phys. Lett.

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.Comment: 6 page

Quantum Reduced Loop Gravity

Quantum Reduced Loop Gravity provides a promising framework for a consistent characterization of the early Universe dynamics. Inspired by BKL conjecture, a flat Universe is described as a collection of Bianchi I homogeneous patches. The resulting quantum dynamics is described by the scalar constraint operator, whose matrix elements can be analytically computed. The effective semiclassical dynamics is discussed, and the differences with Loop Quantum Cosmology are emphasized

Dixon-Souriau equations from a 5-dimensional spinning particle in a Kaluza-Klein framework

The dimensional reduction of Papapetrou equations is performed in a 5-dimensional Kaluza-Klein background and Dixon-Souriau results for the motion of a charged spinning body are obtained. The splitting provides an electric dipole moment, and, for elementary particles, the induced parity and time-reversal violations are explained.Comment: 20 pages, to appear on Physics Letters

Low-energy sector of 8-dimensional General Relativity: Electro-Weak model and neutrino mass

In a Kaluza-Klein space-time $V^{4}\otimes S^{3}$, we demonstrate that the dimensional reduction of spinors provides a 4-field, whose associated SU(2) gauge connections are geometrized. However, additional and gauge-violating terms arise, but they are highly suppressed by a factor $\beta$, which fixes the amount of the spinor dependence on extra-coordinates. The application of this framework to the Electro-Weak model is performed, thus giving a lower bound for $\beta$ from the request of the electric charge conservation. Moreover, we emphasize that also the Higgs sector can be reproduced, but neutrino masses are predicted and the fine-tuning on the Higgs parameters can be explained, too.Comment: 14 pages, 1 figure, to appear on Int. J. Mod. Phys.

Elementary particle interaction from a Kaluza-Klein scheme

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure. Finally applications to the Electro-Weak model are presented.Comment: 8 pages, Proceedings of the II Stueckelberg worksho