Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor

We show how to "concatenate" variational principles over dierent bases into one over a single base, thereby providing a unied Lagrangian treatment of interacting systems. As an example we study a Klein{ Gordon eld interacting with a mesically charged particle. We employ our method to give a novel group-theoretic derivation of the kinetic stress-energy-momentum tensor density corresponding to the particle

RELIGIOUS EXPERIENCE, LANGUAGE AND FREEDOM

Se percibe en el mundo académico de la teología y de la praxis pastoral, un giro general y englobante hacia el sujeto, la experiencia, la donación del amor, la misericordia, el mundo vivido de los hombres y la vivencia de la fe en la vida cotidiana de un mundo secularizado. Es un anhelo de salir de la simple conceptualización y de las discusiones sin fin sobre la fe, para dar paso a una vivencia y a una experiencia de lo creído y a un testimonio que lo haga creíble. La revolución que ha propiciado el papa Francisco se fundamenta en una radicalidad del seguimiento de Jesús en la vida diaria, en las cosas sencillas, sin muchos malabares teológicos, y sí con una insistencia grande en el amor misericordioso de Dios. Este artículo quiere presentar algunas reflexiones que ayuden a fundamentar la donación experiencial del amor misericordioso, preguntándose por la experiencia, el lenguaje usado para expresarla y la libertad como respuesta del sujeto llamado en el momento del evento

A meeting-point between mathematics and the theory of musical scales: well-formed scales.(Spanish: Un encuentro entre las matemáticas y la teoría de escalas musicales: Escalas bien formadas)

Depto. de Álgebra, Geometría y TopologíaInstituto de Matemática Interdisciplinar (IMI)Fac. de Ciencias MatemáticasTRUEpu

Discrete Lagrangian field theories on Lie groupoids

We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and derive the field equations from a variational principle. We also show that the solutions of these equations are multisymplectic in the sense of Bridges and Marsden. The groupoid framework employed here allows us to recover not only some previously known results on discrete multisymplectic field theories, but also to derive a number of new results, most notably a notion of discrete Lie-Poisson equations and discrete reduction. In a final section, we establish the connection with discrete differential geometry and gauge theories on a lattice.Comment: 37 pages, 6 figures, uses xy-pic (v3: minor amendment to def. 3.5; remark 3.7 added

Homogeneous algebraic distributions

Let p:E→M be a vector bundle of dimension n+m and (xλ,yi), λ=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the type X=∑mi=1Pi∂/∂yi, where Pi are polynomials [respectively, homogeneous polynomials of degree d] in coordinates yi. A vertical distribution over E is said to be algebraic [respectively, homogeneous algebraic of degree d] if all local generators are homogeneous algebraic [respectively, homogeneous algebraic of the same degree d] vector fields. It is proved that a vertical distribution locally spanned by vector fields X1,…,Xr is homogeneous algebraic of degree d if and only if an r×r matrix A=(aij), aij∈C∞(E), exists which is equal to d−1 times the identity matrix along the zero section of E, and such that [χ,Xj]=∑ri=1aijXi, j=1,…,r, where χ is the Liouville vector field

Hamiltonian structure of gauge-invariant variational problems

Let C→M be the bundle of connections of a principal bundle on M . The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density Λ on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle structure over the set of solutions to Euler–Lagrange equations for Λ . This structure is also studied for the Jacobi fields and for the moduli space of extremals