Legendre expansion of the neutrino-antineutrino annihilation kernel: Influence of high order terms

We calculate the Legendre expansion of the rate of the process $\nu + \bar{\nu} \leftrightarrow e^+ + e^-$ up to 3rd order extending previous results of other authors which only consider the 0th and 1st order terms. Using different closure relations for the moment equations of the radiative transfer equation we discuss the physical implications of taking into account quadratic and cubic terms on the energy deposition outside the neutrinosphere in a simplified model. The main conclusion is that 2nd order is necessary in the semi-transparent region and gives good results if an appropriate closure relation is used.Comment: 14 pages, 4 figures. To be published in A&A Supplement Serie

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

Faddeev-Jackiw approach to gauge theories and ineffective constraints

The general conditions for the applicability of the Faddeev-Jackiw approach to gauge theories are studied. When the constraints are effective a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev-Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that the Dirac Hamiltonian can be enlarged to an Extended Hamiltonian including all first class constraints, without changes in the dynamics) and we suggest that when the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the correct dynamics. Finally we present some examples that illustrate this inequivalence.Comment: 21 pages, Latex. To be published in Int. J. Mod. Phys.

Local rectification of heat flux

We present a chain-of-atoms model where heat is rectified, with different fluxes from the hot to the cold baths located at the chain boundaries when the temperature bias is reversed. The chain is homogeneous except for boundary effects and a local modification of the interactions at one site, the "impurity". The rectification mechanism is due here to the localized impurity, the only asymmetrical element of the structure, apart from the externally imposed temperature bias, and does not rely on putting in contact different materials or other known mechanisms such as grading or long-range interactions. The effect survives if all interaction forces are linear except the ones for the impurity.Comment: 5 pages, 5 figure

Proceedings of the 2nd Iberian Nuclear Astrophysics Meeting on Compact Stars

This volume contains most of the links to the presentations delivered at this international workshop. This meeting was the second in the series following the previous I Encuentro Ib\'erico de Compstar, held at the University of Coimbra, Portugal in 2010. The main purpose of this meeting was to strengthen the scientific collaboration between the participants of the Iberian and the rest of the southern European branches of the European Nuclear Astrophysics network, formerly, COMPSTAR. This ESF (European Science Foundation) supported network has been crucial in helping to make a broader audience for the the most interesting and relevant research lines being developed currently in Nuclear Astrophysics, especially related to the physics of neutron stars. The program of the meeting was tailored to theoretical descriptions of the physics of neutron stars although some input from experimental observers and other condensed matter and optics areas of interest was also included.Comment: Journal of Physics: Conference Series Volume 342 (2012), Proceedings of the 2nd Iberian Nuclear Astrophysics Meeting on Compact Stars, 22-23 September 2011, Salamanca-Spain. Editors, M. A. Perez-Garcia, J. Pons and C. Albertus Editor

Evolutionary Laws, Initial Conditions, and Gauge Fixing in Constrained Systems

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and the determination of inequivalent initial data. The Lagrangian discussion is novel, and a proof is given that the final number of degrees of freedom in the two formulations agrees. We give applications to reparameterization invariant theories, where we prove that one of the constraints must be explicitly time dependent. We illustrate our procedure with the examples of trajectories in spacetime and with spatially homogeneous cosmological models. Finally, we comment briefly on Dirac's extended Hamiltonian technique.Comment: 23 pages; plain TeX. To appear: Classical & Quantum Gravit