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

Explicit Comparison Theorems for D -modules

We prove in an explicit way a duality formula between two A2-modules Mlog and Mflog associated to a plane curve and we give an application of this duality to the comparison between Mflog and the A2-module of rational functions along the curve. We treat the analytic case as well

On the computation of Bernstein–Sato ideals

In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations in a Poincar´e–Birkhoff–Witt algebra—with the readily available method of Oaku and Takayama. We show that it can deal with interesting examples that have proved intractable so far.Ministerio de Ciencia y Tecnología BFM-2001-3164Junta de Andalucía FQM-33

HAWC response to atmospheric electricity activity

The HAWC Gamma Ray observatory consists of 300 water Cherenkov detectors (WCD) instrumented with four photo multipliers tubes (PMT) per WCD. HAWC is located between two of the highest mountains in Mexico. The high altitude (4100 m asl), the relatively short distance to the Gulf of Mexico (~100 km), the large detecting area (22 000 m$^2$) and its high sensitivity, make HAWC a good instrument to explore the acceleration of particles due to the electric fields existing inside storm clouds. In particular, the scaler system of HAWC records the output of each one of the 1200 PMTs as well as the 2, 3, and 4-fold multiplicities (logic AND in a time window of 30 ns) of each WCD with a sampling rate of 40 Hz. Using the scaler data, we have identified 20 enhancements of the observed rate during periods when storm clouds were over HAWC but without cloud-earth discharges. These enhancements can be produced by electrons with energy of tens of MeV, accelerated by the electric fields of tens of kV/m measured at the site during the storm periods. In this work, we present the recorded data, the method of analysis and our preliminary conclusions on the electron acceleration by the electric fields inside the clouds.Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Korea. See arXiv:1708.02572 for all HAWC contribution

Geometry of Lagrangian First-order Classical Field Theories

We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the {\sl Euler-Lagrange equations} in two equivalent ways: as the result of a variational problem and developing the {\sl jet field formalism} (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied.Comment: Latex file, 48 page