Non Relativistic Limit of a Model of Fermions interacting through a Chern-Simons Field

We study the non relativistic limit of a Model of Fermions interacting through a Chern-Simons Field, from a perspective that resembles the Wilson's Renormalization Group approach, instead of the more usual approach found in most texts of Field Theory. The solution of some difficulties, and a new understanding of non relativistic models is given.Comment: 16 pages (revtex), 5 figures (eps). Invited talk at the meeting ``II Trends in Theoretical Physics'', Buenos Aires, Dec. 1998. To be published by AI

Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics

We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.Comment: 12 pages, 7 figure

Finite Rotations

We present an elementary discussion of two basic properties of angular displacements, namely, the anticommutation of finite rotations and the commutation of infinitesimal rotations, and show how commutation is achieved as the angular displacements get smaller and smaller

Flag-Dipole Spinor Fields in ESK Gravities

We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on $f(R)$ and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given for instance by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle.Comment: 18 pages, improved versio