Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phase-space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of General Relativity, or other generally covariant theories, only closes as a soft algebra and not a a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra --with structure constants-- but a soft algebra --with structure {\it functions}.Comment: 22 pages, version to be published in Classical & Quantum Gravit

Population Synthesis of Isolated Neutron Stars with magneto-rotational evolution II: from radio-pulsars to magnetars

Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include $X$-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, simultaneously, reproduce the characteristics of the radio-pulsar distribution. However, even considering the most favourable magneto-thermal evolution models with fast field decay, log-normal distributions of the initial magnetic field over-predict the number of visible sources with periods longer than 12 s. We then show that the problem can be solved with different distributions of magnetic field, such as a truncated log-normal distribution, or a binormal distribution with two distinct populations. We use the observational lack of isolated NSs with spin periods P>12 s to establish an upper limit to the fraction of magnetars born with B > 10^{15} G (less than 1\%). As future detections keep increasing the magnetar and high-B pulsar statistics, our approach can be used to establish a severe constraint on the maximum magnetic field at birth of NSs.Comment: 12 pages, 11 figures, 5 table

Image Analysis and Multiphase Bioreactors

The applications of visualisation and image analysis to bioreactors can be found in two main areas: the characterisation of biomass (fungi, bacteria, yeasts, animal and plant cells, etc), in terms of size, morphology and physiology, that is the far most developed, and the characterisation of the multiphase behaviour of the reactors (flow patterns, velocity fields, bubble size and shape distribution, foaming), that may require sophisticated visualisation techniques

Ag-coverage-dependent symmetry of the electronic states of the Pt(111)-Ag-Bi interface: The ARPES view of a structural transition

We studied by angle-resolved photoelectron spectroscopy the strain-related structural transition from a pseudomorphic monolayer (ML) to a striped incommensurate phase in an Ag thin film grown on Pt(111). We exploited the surfactant properties of Bi to grow ordered Pt(111)-xMLAg-Bi trilayers with 0 < x < 5 ML, and monitored the dispersion of the Bi-derived interface states to probe the structure of the underlying Ag film. We find that their symmetry changes from threefold to sixfold and back to threefold in the Ag coverage range studied. Together with previous scanning tunneling microscopy and photoelectron diffraction data, these results provide a consistent microscopic description of the coverage-dependent structural transition.Comment: 10 pages, 9 figure

Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincar\'e invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincar\'e symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincar\'e. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincar\'e invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved bakground.Comment: 31 pa

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions in a previously developed MC code to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.Comment: 6 pages, 4 figures To appear in Proceedings of II Iberian Nuclear Astrophysics Meeting held in Salamanca, September 22-23, 201

Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of {\it external} relativistic center of mass can be defined only in terms of the {\it external} Poincar\'e group realization. Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the Poincar\'e group is defined. The three concepts of {\it internal} center of mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An adapted canonical basis of relative variables is found. The invariant mass is the Hamiltonian for the relative motions. In this framework we can introduce the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it spin frame} and {\it canonical spin bases} for the rotational kinematics developed for the non-relativistic N-body problem.Comment: 78 pages, revtex fil

Stable quark stars beyond neutran stars : can they account for the missing matter ?

The structure of a spherically symmetric stable dark 'star' is discussed, at zero temperature, containing 1) a core of quarks in the deconfined phase and antileptons 2) a shell of hadrons in particular $n$, $p$, $\Lambda$ and $\Sigma^-$ and leptons or antileptons and 3) a shell of hydrogen in the superfluid phase. If the superfluid hydrogen phase goes over into the electromagnetic plasma phase at densities well below one atom / $(10 fm)^{3}$, as is usually assumed, the hydrogen shell is insignificant for the mass and the radius of the 'star'. These quantities are then determined approximatively : mass = 1.8 solar masses and radius = 9.2 km. On the contrary if densities of the order of one atom / $(10 fm)^{3}$ do form a stable hydrogen superfluid phase, we find a large range of possible masses from 1.8 to 375 solar masses. The radii vary accordingly from 9 to 1200 km.Comment: 5 pages, 2 figures, contribution to Strange Quark Matter conference, Frankfurt, Germany, Sept. 200