A Unified Approach to High Density: Pion Fluctuations in Skyrmion Matter

As the first in a series of systematic work on dense hadronic matter, we study the properties of the pion in dense medium using Skyrme's effective Lagrangian as a unified theory of the hadronic interactions applicable in the large $N_c$ limit. Dense baryonic matter is described as the ground state of a skyrmion matter which appears in two differentiated phases as a function of matter density: i) at high densities as a stable cubic-centered (CC) half-skyrmion crystal; ii) at low densities as an unstable face-centered cubic (FCC) skyrmion crystal. We substitute the latter by a stable inhomogeneous phase of lumps of dense matter, which represents a naive Maxwell construction of the phase transition. This baryonic dense medium serves as a background for the pions whose effective {\em in-medium} Lagrangian we construct by allowing time-dependent quantum fluctuations on the classical dense matter field. We find that the same parameter which describes the phase transition for baryonic matter, the expectation value of the $\sigma$ field, also describes the phase transition for the dynamics of the {\em in-medium} pion. Thus, the structure of the baryonic ground state $crucially$ determines the behavior of the pion in the medium. As matter density increases, $$ decreases, a phenomenon which we interpret to signal, in terms of the parameters of the effective pion Lagrangian $f_\pi^*$ and $m_\pi^*$, the restoration of chiral symmetry at high density. Our calculation shows also the important role played by the higher powers in the density as it increases and chiral symmetry is being restored. This feature is likely to be generic at high density although our ground state may not be the true ground state

Atiyah-Manton Approach to Skyrmion Matter

We propose how to approach, and report on the first results in our effort for, describing nuclear matter starting from the solitonic picture of baryons which is supposed to represent QCD for large number of colors. For this purpose, the instanton-skyrmion connection of Atiyah and Manton is exploited to describe skyrmion matter. We first modify 't Hooft's multi-instanton solution so as to suitably incorporate proper dynamical variables into the skyrmion matter and then by taking these variables as variational parameters, we show that they cover a configuration space sufficient to adequately describe the ground state properties of nuclear matter starting from the skyrmion picture. Our results turn out to be comparable to those so far found in different numerical calculations, with our solution reaching stability at high density for a crystal structure and obtaining a comparable value for the energy per baryon at the minimum, thus setting the stage for the next step

Public Expenditure in Valledupar during the Periods 2012- 2015 y 2016-2019

36 páginas.El gasto púbico es un concepto utilizado en nuestro país que tiene como significado la cantidad de dinero que puede utilizar un gobierno para resolver las necesidades de una sociedad, es importante porque con un buen uso del gasto público se podría llegar más personas y más población, teniendo en cuenta que Colombia y muchos sectores de la sociedad cuentan con carencias en la obtención de los servicios básicos que es obligación del gobierno nacional y de los gobiernos locales, por medio de esta investigación se pretende dar a conocer la importancia del gasto público nacional local y municipal, reconociendo la importancia de su buen manejo para la prosperidad de la sociedad en que se aplique.Public spending is a concept used in our country that has as its meaning the amount of money that a government can use to solve the needs of a society, it is important because with a good use of public spending it could reach more people and more population, taking into account that Colombia and many sectors of society have many shortcomings in obtaining basic services that is the obligation of the national government and local governments, through this research we want to publicize the importance of local national public expenditure and municipal, recognizing the importance of its good management for the prosperity of the society in which it is applied