Theories in More than Four Dimensions

Particle physics models where there are large hidden extra dimensions are currently on the focus of an intense activity. The main reason is that these large extra dimensions may come with a TeV scale for quantum gravity (or string theory) which leads to a plethora of new observable phenomena in colliders as well in other areas of particle physics. Those new dimensions could be as large as millimeters implying deviations of the Newton's law of gravity at these scales. Intending to provide a basic introduction to this fast developing area, we present a general overview of theories with large extra dimensions. We center our discussion on models for neutrino masses, high dimensional extensions of the Standard Model and gauge coupling unification. We discuss the recently proposed technic of splitting fermion wave functions on a tick brane which may solve the problem of a fast proton decay and produce fermion mass hierarchies without invoking extra global symmetries. Randall-Sundrum model and some current trends are also commented.Comment: LaTeX file, 31 pages, no figures. Minor changes, References added. Lectures given at the IX Mexican School on Particles and Fields, Metepec, Puebla, Mexico, August, 2000. To appear in the proceeding

Theory of Phonon-Assisted Multimagnon Optical Absorption and Bimagnon States in Quantum Antiferromagnets

We calculate the effective charge for multimagnon infrared (IR) absorption assisted by phonons in a perovskite like antiferromagnet and we compute the spectra for two magnon absorption using interacting spin-wave theory. The full set of equations for the interacting two magnon problem is presented in the random phase approximation for arbitrary total momentum of the magnon pair. The spin wave theory results fit very well the primary peak of recent measured bands in the parent insulating compounds of cuprate superconductors. The line shape is explained as being due to the absorption of one phonon plus a new quasiparticle excitation of the Heisenberg Hamiltonian that consists off a long lived virtual bound state of two magnons (bimagnon). The bimagnon states have well defined energy and momentum in a substantial portion of the Brillouin zone. The higher energy bands are explained as one phonon plus higher multimagnon absorption processes. Other possible experiments for observing bimagnons are proposed. In addition we predict the line shape for the spin one system La$_2$NiO$_4$.Comment: Modified version of the paper to be published in PR

GUTs and String-GUTs

We look for a connection between string theories and Grand Unified Theories (GUTs), with the aim to look for new insights in the existing four dimensional string-GUT problems. We argue that the construction of consistent string-GUT models could require the use of non canonical affine levels. We list the most common level values related to realistic GUTs.Comment: 8 pages, Latex file, no figures. Acepted for publication in Europhysics Letter

Effects of Lorentz invariance violation on cosmic ray photon emission and gamma ray decay processes

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission rate have a dependency on the cosmic ray primary mass and the electric charge that could modify the UHECR spectrum. Furthermore, LIV dramatically enhances photon decay into an electro-positron pair above certain energy threshold. This last effect can then be used to set limits to the LIV energy scale from the direct observation of very high energy cosmic photon events by telescopes of gamma-rays.Comment: Proceedings of the 35th International Cosmic Ray Conference (ICRC 2017), Busan, Kore