60 research outputs found
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
Low-energy sector of 8-dimensional General Relativity: Electro-Weak model and neutrino mass
In a Kaluza-Klein space-time , 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 , 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 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.
Towards Loop Quantum Gravity without the time gauge
The Hamiltonian formulation of the Holst action is reviewed and it is
provided 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.Comment: 5 pages, accepted for publication in Phys. Rev. Let
A critical analysis of the cosmological implementation of Loop Quantum Gravity
This papers offers a critical discussion on the procedure by which Loop
Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG)
theory. Revising recent issues in preserving SU(2) symmetry when quantizing the
isotropic Universe, we trace a new perspective in approaching the cosmological
problem within quantum geometry. The cosmological sector of LQG is reviewed and
a critical point of view on LQC is presented. It is outlined how a polymer-like
scale for quantum cosmology can be predicted from a proper fundamental graph
underlying the homogeneous and isotropic continuous picture. However, such a
minimum scale does not coincide with the choice made in LQC. Finally, the
perspectives towards a consistent cosmological LQG model based on such a graph
structure are discussed.Comment: 11 pages, accepted for publication in Modern Physics Letters
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
Matter in Loop Quantum Gravity without time gauge: a non-minimally coupled scalar field
We analyze the phase space of gravity non-minimally coupled to a scalar field
in a generic local Lorentz frame. We reduce the set of constraints to a
first-class one by fixing a specific hypersurfaces in the phase space. The main
issue of our analysis is to extend the features of the vacuum case to the
presence of scalar matter by recovering the emergence of an SU(2) gauge
structure and the non-dynamical role of boost variables. Within this scheme,
the super-momentum and the super-Hamiltonian are those ones associated with a
scalar field minimally coupled to the metric in the Einstein frame. Hence, the
kinematical Hilbert space is defined as in canonical Loop Quantum Gravity with
a scalar field, but the differences in the area spectrum are outlined to be the
same as in the time-gauge approach.Comment: 6 page
Dirac equations in curved space-time versus Papapetrou spinning particles
We find out classical particles, starting from Dirac quantum fields on a
curved space-time, by an eikonal approximation and a localization hypothesis
for amplitudes. We recover the results by Mathisson-Papapetrou, hence
establishing a fundamental correspondence between the coupling of classical and
quantum spinning particles with the gravitational field.Comment: 6 pages, 1 figure, accepted for publication in Europhysics Letter
Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation
In the work of Kerner et al. (2001) the problem of the geodesic deviation in
a 5D Kaluza Klein background is faced. The 4D space-time projection of the
resulting equation coincides with the usual geodesic deviation equation in the
presence of the Lorenz force, provided that the fifth component of the
deviation vector satisfies an extra constraint which takes into account the
conservation along the path. The analysis was performed setting as a
constant the scalar field which appears in Kaluza-Klein model. Here we focus on
the extension of such a work to the model where the presence of the scalar
field is considered. Our result coincides with that of Kerner et al. when the
minimal case is considered, while it shows some departures in the
general case. The novelty due to the presence of is that the variation
of the between the two geodesic lines is not conserved during the motion;
an exact law for such a behaviour has been derived.Comment: 9 page
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