Propagating torsion in the Einstein frame

The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume element so that it is compatible with the connection. The condition of connection compatibility gives constraints on torsion, which are also necessary for the consistence of torsion, minimal coupling, and electromagnetic gauge invariance. To solve the problem of positivity of energy associated with the torsionic scalar, we reformulate this theory in the Einstein conformal frame. In the presence of the electromagnetic field, we obtain the Hojman-Rosenbaum-Ryan-Shepley theory of propagating torsion with a different factor in the torsionic kinetic term.Comment: 10 pages; published versio

The Maxwell Lagrangian in purely affine gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein-Maxwell equations in the metric-affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.Comment: 9 pages; published versio

Variational formulation of Eisenhart's unified theory

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.Comment: 7 pages; published versio

Interacting dark energy in f(R)f(R) gravity

The field equations in $f(R)$ gravity derived from the Palatini variational principle and formulated in the Einstein conformal frame yield a cosmological term which varies with time. Moreover, they break the conservation of the energy--momentum tensor for matter, generating the interaction between matter and dark energy. Unlike phenomenological models of interacting dark energy, $f(R)$ gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar $R$). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function $f(R)$, and examine how the simplest phenomenological models of a variable cosmological constant are related to $f(R)$ gravity. Particularly, we show that $\Lambda c^2=H^2(1-2q)$ for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form $R-1/R$, which is the simplest way of introducing current cosmic acceleration in $f(R)$ gravity, the predicted matter--dark energy interaction rate changes significantly in time, and its current value is relatively weak (on the order of 1% of $H_0$), in agreement with astronomical observations.Comment: 8 pages; published versio

Towards a Relativistic Description of Exotic Meson Decays

This work analyses hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $\pi_{1}$, in a fully relativistic formalism, and makes comparisons with non-relativistic results. We also discuss Coulomb gauge decays of normal mesons that proceed through their hybrid components. The relativistic spin wave functions of mesons and hybrids are constructed based on unitary representations of the Lorentz group. The radial wave functions are obtained from phenomenological considerations of the mass operator. Fully relativistic results (with Wigner rotations) differ significantly from non-relativistic ones. We also find that the decay channels $\pi_{1}\to\pi b_{1}, \pi f_{1}, KK_{1}$ are favored, in agreement with results obtained using other models.Comment: 14 pages, 7 figure

Quantum simulator for the Schwinger effect with atoms in bi-chromatic optical lattices

Ultra-cold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian describing electrons and positrons in an external electric field. This facilitates the experimental simulation of (so far unobserved) fundamental quantum phenomena such as the Schwinger effect, i.e., spontaneous electron-positron pair creation out of the vacuum by a strong electric field.Comment: 4 pages, 2 figures; minor corrections and improvements in text and in figures; references adde

Nonsingular, big-bounce cosmology from spinor-torsion coupling

The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.Comment: 7 pages; published versio

Gravitation, electromagnetism and the cosmological constant in purely affine gravity

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric-affine pictures, unless the electromagnetic field couples to the cosmological constant.Comment: 14 pages, extended and combined with gr-qc/0701176; published versio

Breast-feeding: Current knowledge, attitudes and practices of paediatricians and obstetricians

Doctors, as part of the healthcare team, can have a significant impact on the successful initiation and maintenance of breastfeeding. There is a need for ongoing education and intervention programmes to update current knowledge on breastfeeding management

Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations