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We present a tetrad–affine approach to f ( Q ) gravity coupled to spinor fields of spin- 1 2 . After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind f ( Q ) = α Q n . At late time such solutions are seen to isotropize and, depending on the value of the exponent n, they can undergo an accelerated expansion of the spatial scale factors.

We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $\overline{\psi}\psi=0$ with non-vanishing bi-linear pseudo-scalar $i\overline{\psi}\gamma^5\psi\not=0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations., Comment: 12 pages

Making use of the modern techniques of non-holonomic geometry and constrained variational calculus, a revisitation of Ostrogradsky's Hamiltonian formulation of the evolution equations determined by a Lagrangian of order >= 2 in the derivatives of the configuration variables is presented., 8 pages

Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with respect to Einstein--Cartan--Sciama--Kibble theory $\left(f(R)=R\right)$ are outlined., Comment: 13 pages

We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime while the spinor field is a flag-dipole., 12 pages

The Hamiltonian formulation of the theory proposed in [1, 2] is given both in the Hamilton–De Donder and in the multimomentum Hamiltonian geometrical approaches. (3 + 3) Yang–Mills gauge theories are dealt with explicitly in order to restate them in terms of Einstein–Cartan like field theories.

We show howp-adic analysis can be used in some cases to treat divergent series in quantum mechanics. We consider examples in which the usual theory of the Schrodinger equation would give rise to an infinite expectation value of the energy operator. By usingp-adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy. We present also the main ideas to interpret a quantum mechanical state by means ofp-adic statistics.

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against sensitivities of VIRGO, LIGO and LISA interferometers., 12 pages, 4 figures

We discuss the f(R)-theories of gravity with torsion in the framework of jet-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber jet-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang--Mills fields and spin perfect fluid. Such fields enlarge the jet-bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories., 17 pages

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe., 12 pages

The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory., 8 Pages, Submitted to International Journal of Geometric Methods in Modern Physics

In the gauge natural bundle framework a new space is introduced and a first-order purely frame-formulation of General Relativity is obtained., Comment: 9 Pages, Submitted to Classical and Quantum Gravity

We present an analysis of the phase space of cosmological models based on a non minimal coupling between the geometry and a fermionic condensate. We obtain that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models and at the same time guarantees an evolution towards a state indistinguishable from General Relativistic cosmological models. In this light, we show how the use of some specific potentials is able to reproduce naturally two de Sitter phases separated by a power law expansion which could be an interesting model for the unification of an inflationary phase and a dark energy era., 25 pages, 4 figures, submitted to Classical and Quantum Gravity

The Eastbrooke Whalquist definition of a spatial tensor analysis is compared with Massa's. It is shown that the second approach includes the first one as a special one. Lavoro eseguito nell'ambito dell'attivita del Gruppo Nazionale della Fisica Matematica del C.N.R.

A coordinate-dependent investigation of limits of space-times is given. Different kinds of limits are found and analyzed. A criterion selecting limits which appear to be nothing but “technical tricks” is proposed. Finally, a method for generating new limits from a given family of metrics is examined.

A mathematically consistent global theory of super fibre bundles is laid down. In this framework the authors perform, in a rigorous way, the analysis of the construction of super fibre bundles, connections, reduced bundles and reduced connections. Some bundles of physical interest, constructed over a supermanifold (the Lorentz bundle and the graded Poincare bundle), are analysed in detail. A criterion for the existence of a Lorentz bundle over a supermanifold is established. Some results about subgroups of super Lie groups are also given.