A systematization for one-loop 4D Feynman integrals

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.     

Hybrid RSiO1.5/B2O3 Gels from Modified Silicon Alkoxides and Boric Acid

A new sol-gel route, without any external water addition, for the preparation of hybrid RSiO_1.5/B₂O₃ gels (R = Me, Et, Vi) is reported. The gels are easily synthesized by reacting B(OH)₃ with the liquid silicon alkoxide. The gels have been characterized mainly by FT-IR and ¹¹B MAS NMR spectroscopy. The results show that this new sol-gel process allows the formation of a homogeneous borosilicate gel in which trigonal BO₃ units are incorporated into the siloxane network via B—O—Si bonds.