Hamilton-Jacobi Theory in k-Symplectic Field Theories

In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework

Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page

Spectral analysis of Markarian 421 and Markarian 501 with HAWC

The Hight Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory monitors the gamma-ray sky in the energy range from 100 GeV to 100 TeV and has detected two very high energy (VHE) blazars: Markarian 421 (Mrk 421) and Markarian 501 (Mrk 501) in 1.5 years of observations. In this work, we present the spectral analysis above 1 TeV of both sources using a maximum likelihood method and an artificial neural network as an energy estimator. The main objectives are to constrain the spectral curvature of Mrk 421 and Mrk 501 at $\sim$5 TeV using the EBL models from Gilmore et al. (2012) and Franceschini et al. (2008).Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Korea. See arXiv:1708.02572 for all HAWC contribution

A semi-infinite matrix analysis of the BFKL equation

The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green's function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution with energy compatible with unitarity.Comment: Small changes, same conclusions, matching the published version in EPJ

On the Multimomentum Bundles and the Legendre Maps in Field Theories

We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures) are analyzed and compared. The corresponding Legendre maps are introduced. As a consequence, the definition of regular and almost-regular Lagrangian systems is reviewed and extended from different but equivalent ways.Comment: LaTeX file, 19 pages. Replaced with the published version. Minor mistakes are correcte

Solitary Waves in Massive Nonlinear S^N-Sigma Models

The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional Neumann mechanical problem. There are topological (heteroclinic trajectories) and non-topological (homoclinic trajectories) kinks. The stability of some embedded sine-Gordon kinks is discussed by means of the direct estimation of the spectra of the second-order fluctuation operators around them, whereas the instability of other topological and non-topological kinks is established applying the Morse index theorem

An Approach to Publish Spatial Data on the Web: The GeoLinked Data Case

In this paper we report on an ongoing process aimed at publishing hydrographical data on the Web with a Spanish GeoLinked Data Use Case. Moreover, we discuss the process we followed, and propose methodological guidelines for all the activities involved within the process