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Since Pauli's hypothesis of their existence in 1930, neutrinos never ceased to bring into play novel ideas and to add new pieces of physics in the whole picture of fundamental interactions. They are only weakly interacting and, at odds with Standard Model's predictions, have a mass less than one millionth of the electron mass, which makes the investigation of their properties very challenging. The issue of the measurement of neutrino's rest mass gained a wider and wider consensus since its discovery through neutrino oscillations in 1998. Various neutrino sources are available for experiments, ranging from nuclear collisions of cosmic rays in the Earth atmosphere and supernova explosions to neutrino beams produced by accelerators and power reactors. These suggest different approaches to the experimental detection and measurement of the absolute value of the neutrino mass. In this paper, we retrace the intriguing story of this endeavor, focusing mainly on direct mass determination methods. The puzzling issue of the nature of massive neutrinos is addressed as well with explicit reference to the phenomenon of double beta-decay as a viable experimental tool to discriminate between Dirac's and Majorana's nature. [ABSTRACT FROM AUTHOR]

The static spherically symmetric traversable wormholes are analysed in the Einstein-Cartan theory of gravitation. In particular, we computed the torsion tensor for matter fields with different spin $ S=0, 1/2, 1, 3/2$ . Interestingly, only for certain values of the spin, the torsion contribution to the Einstein-Cartan field equation allows one to satisfy both flaring-out condition and null energy condition. In this scenario, traversable wormholes can be produced by using usual (non-exotic) spinning matter. [ABSTRACT FROM AUTHOR]

In this paper, we develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method, based on a Taylor expansion of metric and stress-energy tensor components in a neighbourhood of the wormhole throat, reduces the Einstein equation to an infinite set of algebraic conditions, which can be satisfied order by order. The approach easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state. The method is then applied to some relevant examples of exotic matter characterised by a constant energy density and that also show an isotropic behaviour in the stress-energy tensor or obeying to a quintessence-like equation of state. [ABSTRACT FROM AUTHOR]

The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed, which relies upon the method of integration in the complex domain for the solution of hyperbolic equations with variable coefficients. In order to study the propagation of wave fronts, we integrate the equations of bicharacteristics which are null geodesics, and we are able to express them, for the first time in the literature, with the help of elliptic integrals for another choice of Kasner parameters. For generic values of the three Kasner parameters, the solution of the Cauchy problem is built through a pair of integral operators, where the amplitude and phase functions in the integrand solve a coupled system of partial differential equations. The first is the so-called transport equation, whereas the second is a nonlinear equation that reduces to the Eikonal equation if the amplitude is a slowly varying function. Remarkably, the analysis of such a coupled system is proved to be equivalent to building first an auxiliary covariant vector having vanishing divergence, while all nonlinearities are mapped into solving a covariant generalization of the Ermakov-Pinney equation for the amplitude function. Last, from a linear set of equations for the gradient of the phase one recovers the phase itself. This is the parametrix construction that relies upon Fourier-Maslov integral operators, but with a novel perspective on the nonlinearities in the dispersion relation. Furthermore, the Adomian method for nonlinear partial differential equations is applied to generate a recursive scheme for the evaluation of the amplitude function in the parametrix. The resulting formulas can be used to build self-dual solutions to the field equations of noncommutative gravity, as has been shown in the recent literature. [ABSTRACT FROM AUTHOR]

This paper studies nonlinear constitutive equations for gravitoelectromagnetism. Eventually, the problem is solved of finding, for a given particular solution of the gravity-Maxwell equations, the exact form of the corresponding nonlinear constitutive equations. [ABSTRACT FROM AUTHOR]

In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg-Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg-Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector. [ABSTRACT FROM AUTHOR]

A modification of the standard product used in local field theory by means of an associative deformed product is proposed. We present a class of deformed products, one for every spin S = 0, 1/2, 1, that induces a nonlocal theory, displaying different form for different fields. This type of deformed product is naturally supersymmetric and it has an intriguing duality. [ABSTRACT FROM AUTHOR]

Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity parameter θ. The present paper studies the asymptotic behavior of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighborhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler–Poisson–Darboux equation, where the parameter θ affects explicitly the functional form of the source term. Interestingly, for finite values of θ, there is full qualitative agreement with general relativity: the conformal singularity at spacelike infinity reduces in a considerable way the differentiability class of scalar fields at future null infinity. In the physical space-time, this means that the scalar field has an asymptotic behavior with a fall-off going on rather more slowly than in flat space-time. [ABSTRACT FROM AUTHOR]

We give a straightforward generalization of the Ginzburg–Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb–Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity. A physical scenario behind the model proposed, which can be directly tested by experiments, is envisaged. [ABSTRACT FROM AUTHOR]