arXiv subjects
Publications and source records attributed to Luca Fabbri.
Recently we have constructed the conformal gravity with metric and torsion, finding the gravitational field equations that give the conservation laws and trace condition; in the present paper we apply this theory to the case of ELKO matter field, proving that their spin and energy densities once the matter field equations are considered imply the validity of the conservation laws and trace condition mentioned above.
We present a unifying approach where weak forces and neutrino oscillations are interpreted under the same standards of torsional hybrid gravity. This gravitational theory mixes metric and metric-affine formalism in presence of torsion and allows to derive an effective scalar field which gives rise to a running coupling for Dirac matter fields. In this picture, two phenomena occurring at different energy scales can be encompassed under the dynamics of such a single scalar field, which represents the further torsional and curvature degrees of freedom.
We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on $f(R)$ and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given for instance by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle.
In this paper we consider an axial torsion to build metric-compatible connections in conformal gravity, with gauge potentials; the geometric background is filled with Dirac spinors: scalar fields with suitable potentials are added eventually. The system of field equations is worked out to have torsional effects converted into spinorial self-interactions: the massless spinors display self-interactions of a specific form that gives them the features they have in the non-conformal theory but with the additional character of renormalizability, and the mechanisms of generation of mass and cosmological constants become dynamical. As a final step we will address the cosmological constant and coincidence problems.
In this paper we show how in the most natural extension of gravity with torsion, fermion fields are endowed with running coupling in spinorial interaction, that are shown to reproduce the strength and structure of the leptonic weak forces.
In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German \textit{Eigenspinoren des LadungsKonjugationsOperators} designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field's self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.
We analyze the phase space of Bianchi I cosmologies filled by a spin fluid in the framework of $f(R)$-gravity with torsion using a combination of the dynamical systems approach and the 1+3 covariant formalism. In the simple case of $f(R)=R^n$ our results allow a quantification of the role of torsion and the spin of the cosmic fluid in the evolution of the cosmology. While torsion is able to modify the cosmological dynamics with respect to the purely metric case, the spin has little influence on the cosmology. We argue that this is due to the different symmetries of the tensor characterizing the anisotropies and the spin tensor. The cosmological model we analyzed presents isotropization for a wide set of initial conditions and values of the parameters and allows for two types of exotic bounce solutions.
Quite recently it was shown that torsion induces interactions among leptons that are identical to the weak interactions of leptons of the Weinberg standard model, if it is in terms of leptonic bound states that the bosonic sector is built: here we obtain the partially conserved axial currents showing that they are the same of the standard model, if the composite mediators have specific mass relationships: we show that their masses are indeed the measured ones, if reasonable approximations are taken.
In the present paper we consider a theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, we discuss the couplings to Dirac fields and spin fluids: in the case of Dirac fields, we discuss how in our approach, the Dirac self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales, showing different applications according to the value of the parameter we have assigned; in the case of spin fluids, we discuss FLRW cosmological models arising from the proposed theory.
We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem of renormalizability of point-like particles.
In a previous paper we considered the most general field equations for a system of two fermions of which one single-handed, showing that the spin-torsion interactions among these spinors had the same structure of the electroweak forces among leptons; in this paper we consider the most general field equations for a system of two fermions, showing that the spin-torsion interactions among these spinors have a structure similar to that of the electroweak forces among hadrons: possible differences are discussed, and consequently further extensions are speculated.
We study Weyssenhoff spin fluids in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity; the resulting field equations are derived and discussed in both Jordan and Einstein frames, clarifying the role played by the spin and the non-linearity of the gravitational Lagrangian f(R) in generating the torsional dynamical contributions. The general conservation laws holding for f(R)-gravity with torsion are employed to provide the conditions needed to ensure the preservation of the Hamiltonian constraint and the consequent correct formulation of the associated initial value problem. Examples are eventually given.
We consider the Principle of Equivalence along with Weyl theorem to discuss the interpretation of gravity as a geometric effect; we study what are the restrictions on the connections that must be required for this geometrization to occur in the most general case.
We discuss the general structure of metric geometries, and how metricity implies the complete antisymmetry of Cartan tensor; an application in the frame of Lie group theory is given. Interpretations of the completely antisymmetric torsion in physical models are reviewed.
We consider the ESK theory, based on the principle for which the space is filled with matter fields in such a way that Cartan torsion is spin; in the geometry in which Cartan torsion tensor is completely antisymmetric, spin has to be completely antisymmetric: we will show how the complete antisymmetry of spin constraints the form of possible matter field theories as to allow the special case of the simplest one solely, all other most general cases being excluded.
We consider how the principles of causality and equivalence restrict the background in which matter field theories are defined; those constraints develop in restrictions for these matter field theories: the simplest matter field theory aside, all other less simple matter field theories are too complex therefore resulting to be inconsistent in general instances.
In this paper, we start from the geometric relativistic foundations to define the basis upon which matter field theories are built, and their wave solutions are investigated, finding that they display repulsive interactions able to reproduce the exclusion principle in terms of its effects in a dynamical way, then discussing possible consequences and problems.
Starting from a 5D-Riemannian manifold, we show that a reduction mechanism to 4D-spacetimes reproduces Extended Theories of Gravity (ETGs) that are direct generalizations of Einstein's gravity. In this context, the gravitational degrees of freedom can be dealt under the standard of spacetime deformations. Besides, such deformations can be related to the mass spectra of particles. The intrinsic non-linearity of ETGs gives an energy-dependent running coupling, while torsion gives rise to interactions among spinors displaying the structure of the weak forces among fermions. We discuss how this scheme is compatible with the known observational evidence and suggest that eventual discrepancies could be detected in experiments, as ATLAS and CMS, today running at LHC (CERN). We finally discuss the consequences of the present approach in view of unification of physical interactions.