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Within the framework of f(R)=R+αR2 gravity, we study realistic models of neutron stars, using equations of state compatible with the LIGO constraints, i.e., APR4, MPA1, SLy, and WW1. By numerically solving modified Tolman-Oppenheimer-Volkoff equations, we investigate the mass-radius relation in both metric and torsional f(R)=R+αR2 gravity models. In particular, we observe that torsion effects decrease the compactness and total mass of neutron star with respect to the general relativity predictions, therefore mimicking the effects of a repulsive massive field. The opposite occurs in the metric theory, where mass and compactness increase with α, thus inducing an excess of mass that overtakes the standard general relativity limit. We also find that the sign of α must be reversed whether one considers the metric theory (positive) or torsion (negative) to avoid blowing up solutions. This could draw an easy test to either confirm or discard one or the other theory by determining the sign of parameter α.

The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual Dirac spinor. IV, V, VI are those for which the scalar and pseudo-scalar bi-linear spinor quantities are identically zero, its spinors are called singular, and they are split in further sub-classes: IV has no further restrictions, its spinors are called flag-dipole; V is the one for which the spin axial-vector vanishes, its spinors are called flagpole, and among them we find the Majorana spinor; VI is the one for which the momentum antisymmetric-tensor vanishes, its spinors are called dipole, and among them we find the Weyl spinor. In the quest for exact solutions of fully-coupled systems of spinor fields in their own gravity, we have already given examples in the case of Dirac fields and Weyl fields but never in the case of Majorana or more generally flagpole spinor fields. Flagpole spinor fields in interaction with their own gravitational field, in the case of axial symmetry, will be considered. Exact solutions of the field equations will be given., 13 pages

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

In the last dozen years a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the Universe from measured distances, only assuming that the geometry of the can be described by the Friedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshift analysis allows us to put constraints on the cosmographic parameters up to the 5fth order, thus inducing indirect constraints on any gravity theory. Here we are interested in the so called teleparallel gravity theory, f(T). Actually we use the analytical expressions of the present day values of f(T) and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for f(T) and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts (GRB) luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC)., Comment: International Journal of Modern Physics D, 20 pages, 5 figures

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.

A new geometrical framework for tetrad-affine formulation of gravity, pure or coupled with Yang–Mills fields, is proposed. After analyzing the geometrical properties of the new mathematical setting, field equations are deduced from a variational principle in the Poincare–Cartan formalism. A generalized Noether Theorem is stated and classical relationship between symmetries and conserved quantities are recovered in the newer scheme. Some explicit examples are given.

A gauge-independent formulation of the theory developed in J. Phys. A: Math. Gen. 36 8341 (2003) is proposed.

We construct a new geometrical framework for Yang–Mills Lagrangian field theories as an appropriate quotient space of the standard first jet-bundle and investigate the geometrical properties of the resulting mathematical setting. We deduce the field equations from a variational problem formulated through a regular Poincare–Cartan form, thus ensuring the kinematical admissibility of critical sections. We state a generalized Nother theorem and explicitly consider the case of the free Yang–Mills field.

Gaussian measures on infinite-dimensional p-adic spaces are defined and the corresponding L2-spaces of p-adic-valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in such spaces and the formal analogy with the usual Segal representation is discussed. It is found that the parameters of the p-adic infinite-dimensional Weyl group are defined only on some balls. In p-adic Hilbert space, representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. The Hamiltonians with singular potentials are realized as bounded symmetric operators in L2-space with respect to a p-adic Gaussian measure.

A momentum representation for p-adic quantum mechanics is constructed. It uses a Fourier transform in the -space with respect to the p-adic Lebesgue distribution and a study of its properties. The momentum representation is used to investigate the spectral properties of the p-adic momentum operator and to study the (p-adic valued) Schrodinger equation for the p-adic harmonic oscillator.

We propose a physical interpretation for a p-adic picture of reality. According to this interpretation, p-adic numbers describe measurements with a finite accuracy (at the same time, real numbers describe measurements with an infinite accuracy). We consider the representation of the position operator in a p-adic Hilbert space and study the spectrum of this operator.

In this work we show how the Poincare-Cartan form can be used to describe the symmetries of Lagrangian supersymmetric (possibly p-adic) field theories. We show that the existence of the Poincare-Cartan form in supermanifold theory is ensured only in a relevant class of Lagrangian densities. Moreover, we give an abstract characterization of supersymmetric invariance based on the Poincare-Cartan form.

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.

In this paper we show how p -adic analysis can be used, in some cases, to treat divergent series in quantum mechanics. We shall consider examples in which the usual theory of Schrodinger equation would give rise to an infinite for the expectation value of the energy operator; on the contrary, by using p -adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy.

This work is the third one of a series of articles in which the foundations of a p‐adic supermanifold field theory are proposed. In this article p‐adic super‐Lie groups are defined and their properties studied; finally, the p‐adic groups of matrices are analyzed.

We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional $f(R)$-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function $f(R)$; some $f(R)$ models do not isotropize and have no Einstein limit, so that they have no physical significance, whereas for other $f(R)$ models isotropization and Einsteinization occur, and so they are physically acceptable, suggesting that phenomenological arguments may select $f(R)$ models that are physically meaningful; the singularity problem can be avoided, due to the presence of torsion; the general conservation laws holding for $f(R)$-gravity with torsion ensure the preservation of the Hamiltonian constraint, so proving that the initial value problem is well-formulated for these models., Comment: 25 pages, 1 figure

A generalization of the Cauchy-Kowalewsky theorem is obtained for nonlinear evolution equations with (1,1)-supersymmetric time. This theorem ensures the existence and uniqueness of a solution for a large class of superanalytic functions. A generalization of Cartan's technique to the supersymmetric case is also obtained, and by means of it the problem of integrating a system of partial differential equations is transformed into the problem of finding a sequence of integral supermanifolds of lower dimension by means of a succession of integrations based on the Cauchy-Kowalewsky theorem. Evolution equations with (1, 1) time are important for applications to supersymmetric quantum mechanics and field theory, namely, square roots of the Schrodinger and heat-conduction equations. We consider nonlinear generalizations of such equations.

This article is the second part of a work in which p‐adic supermanifold theory is studied; by using the algebraic approach introduced in the first part of this work, p‐adic superdifferential maps are introduced and, by restricting attention to the class of strictly differential maps, the foundation of p‐adic supermanifold theory is developed herein. In particular it is shown that the superfield expansion theorem is no longer true: a superdifferential odd variables map which is not a polynomial is constructed. Finally, tangent space and Lie derivatives are constructed, and it is shown that no complex‐valued fermion field of the p‐adic argument could exist.

A sequence of infinitely generated p‐adic Banach superalgebras and their locally convex projective and inductive limits were constructed; their spectral properties are characterized herein and by studying the algebras of matrices constructed with these superalgebras an exponential map and its inverse can be defined. Some examples of superalgebra with pathological spectral properties are discussed.

f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard General Relativity. Only for f(R)=R^{2}, torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f'(R), which can be expressed also as a nonlinear function of the trace of the matter energy-momentum tensor. We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f(R) gravity, torsion can be a geometric source for acceleration., 13 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

Partial differential equations with supersymmetric (1, 1) time are investigated by means of superspace Cauchy-Kowalewsky and Cartan-Kahler techniques. Theorems for the existence and uniqueness of solutions are found for a particular class of superanalytic functions. The (1, 1) time evolution equations are very important in applications to supersymmetric quantum mechanics and quantum field theory: the square roots of Schrodinger and heat equations. We considered nonlinear analogs of these equations which can be interpreted as square roots of Maslov's nonlinear Schrodinger and heat equations.

The geometrical theory of supermanifolds is developed and applied to the super Lie groups. The resulting structural equations and the adjoint representation are studied and used to find the automorphisms of super Lie groups. The N=1 supergravity symmetry group (the so‐called graded Poincare group) is explicitly studied and possible applications are outlined.

The process of the reduction of a principal fibre bundle P(M, G) to a reduced subbundle Q(M, H) is analysed in view of applications to the description of symmetries of gauge theories. The main idea is to relate symmetries of the nonuniqueness of the reduction by gauging the different ways in which for each fiber the unbroken group H is imbedded into the large group G. Gauge theories encompassing gravitation are especially taken into account.

The classical Frobenius theorem, both in its local and global formulations, is generalised to superanalytic supermanifolds. As an application, it is proved that a coset space G/H (where both G and H are super Lie groups) is a supermanifold. Existence and uniqueness of local flows of tangent vector fields is proved.

An analogue of the classical global third Lie theorem is proved to hold for super Lie groups whose ground Banach—Grassmann algebra is (possibly) infinite-dimensional, provided that this algebra has an ordered basis. It is also proved that the superanalytic structure of a connected super Lie group having a prescribed Lie module is unique, although in a weaker sense than in the case of ordinary Lie groups.

In the paper, first‐order partial differential equations are studied on superspace; the key point is the use of a suitable generalization of the Cartan–Kahler integration theorem on superspace. By means of this result, it is possible to investigate the characteristic fields and the structure of the solutions.

After giving a global, constraint-free Lagrangian formulation of theN=1 superspace supergravity in terms of super fibre bundles and differential forms over a supermanifold, we show that the concept of body manifold of a supermanifold provides a natural manner to reduce the theory to spacetime. This reduction, however, is not canonical, and the various ways in which it can be done give rise to transformations of the field variables which generalise the known invariances of theN=1 spacetime supergravity under supersymmetry transformations and spacetime diffeomorphisms.

The foundations of a variational calculus on fibered supermanifolds are outlined, giving applications to the formulation of superspace field theories. Utiyama theorems and conservation laws related to local gauge and general invariance of the theory are proved.

The method of reduction of a connection form from a principal fibre-bundle to a sub-bundle is studied by considering the null tetrad formalism in space-time and discussing in detail the resulting Generalized Maurer-Cartan Structural Equations.

In view of applications to the formulation of gauge field theories on supermanifolds, we study the relation between the sheaves of functions on a supermanifold M and its body manifold M0, respectively. The nonuniqueness of the local injections t: M0→M is analysed in consideration of its role in supersymmetric field theories. A Banach space structure is given to the set of bounded, supersmooth, Ckfields on M in order to get a rigorous formulation of variational principles for the class of theories under consideration.

The reduction of a connection form ρ from a fiber bundle P to a subbundle Q is examined in detail; defining generalized torsion forms, we show how the usual Maurer–Cartan structural equations have to be modified. Examples and applications to classical general relativity and gauge theories are outlined.

Properties of space-times admitting a two parameter abelian symmetry group acting on a null two-surface are investigated. Within this framework, a class of new solutions of Einstein's vacuum equations are found. Some analogies with the theory of black hole are pointed out.