Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory

We propose a general method for the description of arbitrary single spin-j states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher \partial^{2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz- and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz-tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, \Psi_[ \mu\nu]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2,0)+(0,3/2) as part of \Psi_[\mu\nu] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.Comment: LaTex 34 pages, 1 table, 8 figures. arXiv admin note: text overlap with arXiv:1312.581

Electromagnetic multipole moments of elementary spin-1/2, 1, and 3/2 particles

We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to reproduce representation specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincar\'e covariant projector method. We calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector--spinor representations, attend to the most general non-Lagrangian spin-3/2 currents which are allowed by Lorentz invariance to be of third order in the momenta and construct the linear current equivalent of identical multipole moments of one of them. We conclude that such non-Lagrangian currents are not necessarily more general than the two-term currents emerging within the covariant projector method. We compare our results with those of the conventional Proca-, and Rarita-Schwinger frameworks. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-3/2 in the respective (1,0)$\oplus$(0,1), and (3/2,0)$\oplus$(0,3/2) single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation dependent. In particular, we find the bi-vector $(1,0)\oplus (0,1)$ to be characterized by an electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$, and consequently, to the $W$ boson. Our finding points toward the possibility that the $\rho$ meson could transform as part of an antisymmetric tensor with an $a_{1}$ meson-like state as its representation companion.Comment: 27 pages, 2 figure

Microalbuminuria en pacientes con diabetes tipo 2

La diabetes constituye una afección común en el Paraguay, donde unas 300.000 personas la padecen y aproximadamente otras 500.000 personas presentan un estado previo a la enfermedad. La nefropatía es una de las complicaciones mas graves, que sobreviene por la faltade control de la enfermedad. En la actualidad, el acceso al tratamiento sustitutivo, hemodiálisis y transplante renal ha desplazado a la insuficiencia renal al tercer puesto como causa de muerte del paciente diabético, después de la cardiopatía isquémica y del accidente cerebro vascular. La presencia de microalbuminuria en orina es un claro marcador de riesgo hacia la progresión de las complicaciones de la enfermedad, especialmente las nefropatías. En este estudio la prevalencia demicroalbuminuria hallada en los pacientes diabéticos tipo 2, fue de 34.7%, porcentaje elevado con respeto a la referencia que oscila alrededor del 20 al 40% en la Diabetes tipo 2.Existen factores deriesgo que predisponen al desarrollo de la microalbuminuria y su progresión, como son la duración de la diabetes, la falta de control de la glicemia, la hipertensión arterial, una mala alimentación y eltabaquismo. Con el control de dichos factores se vería reducido el riesgo de avance de la enfermedad. Se observó que a medida que aumenta el tiempo de evolución de la enfermedad aumenta la proporción de pacientes diabéticos con microalbuminuria, acompañados por unprogresivo aumento de la presión arterial

Renormalization of the QED of self-interacting second order spin 1/2 fermions

We study the one-loop level renormalization of the electrodynamics of spin 1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant gauge and including fermion self-interactions, which are dimension four operators in this framework. We show that the model is renormalizable for arbitrary values of the tree level gyromagnetic factor g within the validity region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree level fermion self-interactions, we recover the pure QED of second order fermions, which is renormalizable only for |g|=2. Turning off the electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like model with second order fermions in four space-time dimensions.Comment: 32 pages, 9 figures. Published versio