Photon propagation in noncommutative QED with constant external field

We find dispersion laws for the photon propagating in the presence of mutually orthogonal constant external electric and magnetic fields in the context of the $\theta$-expanded noncommutative QED. We show that there is no birefringence to the first order in the noncommutativity parameter $$ By analyzing the group velocities of the photon eigenmodes we show that there occurs superluminal propagation for any direction. This phenomenon depends on the mutual orientation of the external electromagnetic fields and the noncommutativity vector. We argue that the propagation of signals with superluminal group velocity violates causality in spite of the fact that the noncommutative theory is not Lorentz-invariant and speculate about possible workarounds

Los discípulos

El capítulo sobre el Discipulado del libro “Jesús de Nazaret” se funda en el texto de Marcos 3,13-19. Se divide en estos apartados: elección, convivencia y misión del Reino para curar y expulsar demonios, los doce y demás discípulos; al final se trata a las mujeres como seguidoras de Jesús y la oración como experiencia fundamental del discipulado. Nosotros respetamos esta división, y comentamos o ampliamos o contextualizamos las afirmaciones más importantes. También tenemos en cuenta las referencias a la vida y actividad de los discípulos de Jesús en los demás capítulos del libro, sobre todo el de la Bienaventuranzas.The chapter about the Disciples from the book Jesus of Nazareth is based on the Gospel by Mark 3: 13-19. It is divided into the following sections: election, life together and the Kingdom’s mission related to curing and expelling demons, the twelve and other disciples. Finally, it deals with Jesus Christ’s female followers and also praying as the disciples’ fundamental experience. We are respectful of that division. Moreover, we comment, widen and put in context the most important statements. Resides, we take into account all references made in the other chapters on the lives and activities of Christ’s disciples, mainly those made in the text containing the Beatitudes

Boundary-Domain Integral Equations for the diffusion equation in inhomogeneous media based on a new family of parametrices

A mixed boundary value problem for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed by Mikhailov in [15,19] and Chkadua, Mikhailov, Natroshvili in [2]. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators lead to interesting conclusions.Comment: We provide an erratum where we improve upon our previous definition of odd paragrassmann algebra

Soliton fermionic number from the heat kernel expansion

Producción CientíficaWe consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized η function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in amulti flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients.Juant de Castilla y León grant BU 229P18