Francesco Cianfrani

Quantum-Reduced Loop Gravity: Cosmology

We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

Towards Loop Quantum Gravity without the Time Gauge

The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.

Quantum reduced loop gravity: Universe on a lattice

We describe the quantum flat universe in QRLG in terms of states based at cuboidal graphs with six-valent nodes. We investigate the action of the scalar constraint operator at each node and we construct proper semiclassical states. This allows us to discuss the semiclassical effective dynamics of the quantum universe, which resembles that of LQC. In particular, the regulator is identified with the third root of the inverse number of nodes within each homogeneous patch, while inverse-volume corrections are enhanced.

Gauge theories as a geometrical issue of a Kaluza-Klein framework

We present a geometrical unification theory in a Kaluza–Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, in order to make possible to introducing matter just through free spinorial fields. Then we present the applications to (i) a pentadimensional manifold V4 ⊗ S1 so reproducing the original Kaluza–Klein theory with some extensions related to the rule of the scalar field contained in the metric and to the introduction of matter through spinors with a phase dependance from the fifth coordinate, (ii) a seven-dimensional manifold V4 ⊗ S1 ⊗ S2, in which we geometrize the electroweak model by introducing two spinors for every leptonic family and quark generation and a scalar field with two components with opposite hypercharge responsible for spontaneous symmetry breaking.

Generally covariant formulation of Relative Locality in curved spacetime

Institute for Theoretical Physics, University of Wroc law,Pl. Maksa Borna 9, Pl{50-204 Wroc law, Poland(Dated: January 15, 2014)We construct a theory of particles moving in curved both momentum space and spacetime,being a generalization of Relative Locality. We nd that in order to construct such theory,with desired symmetries, including the general coordinate invariance, we have to use nonlocal position variables. It turns out that free particles move on geodesics and momentumdependent translations of Relative Locality are replaced with momentum dependent geodesicdeviations.I. INTRODUCTIONIn the recent years the largely forgotten idea that momentum space may have a nontrivial geometricstructure, known under the name of Born reciprocity [1], has been revived in many di erent guises in thecontext of quantum gravity. It was noticed in [2] that there is a one-to-one correspondence between space-time noncommutativity, expected to be one of the features of quantum gravity, and nontrivial geometricstructures in momentum space. This general observation is supported by explicit calculations done in thecontext of gravity in 2+1 dimensions [3], [4]. Few years later it was realized that many nontrivial features ofDoubly Special Relativity class of theories [5], [6], [7] can be conveniently described in terms of the geometryof de Sitter momentum space [8].Relative Locality [9], [10], [11] is a theoretical framework that has its roots in Born reciprocity. In thisframework the momentum space is brought to foreground. It is rst observed that most, if not all, physicalmeasurements correspond, in fact, to momentum space data. Second it is noticed that the emergence ofa nontrivial geometry in momentum space requires, as a prerequisite, the presence of a mass scale. Suchscale must be provided by a fundamental theory, and it was assumed that there exists a regime of quantumgravity, in which the length scale, the Planck length, is negligibly small, while the mass scale, the Planckmass, remains nite.In the couple of years that passed since Relative Locality was rst proposed the bulk of research investi-gated systems de ned on at Minkowski spacetime. The question arises however if curved momentum spacecould coexists with a nontrivial geometry of spacetime. This possibility is particularly intriguing from the

Quantum-Reduced Loop-Gravity: Relation with the Full Theory

The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects states based on reduced graphs with Livine-Speziale coherent intertwiners and could simplify the analysis of the dynamics in the full theory.

Shortcomings of the big bounce derivation in loop quantum cosmology

We give a prescription to define in loop quantum gravity the electric field operator related to the scale factor of a homogeneous and isotropic cosmological space-time. This procedure allows us to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in loop quantum cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.

Quantum reduced loop gravity and the foundation of loop quantum cosmology

Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.

LOW-ENERGY SECTOR OF EIGHT-DIMENSIONAL GENERAL RELATIVITY: ELECTROWEAK MODEL AND NEUTRINO MASS

In a Kaluza-Klein space-time

Dirac equations in curved space-time vs. Papapetrou spinning particles

V^{4}\otimes S^{3}