Extending invariant complex structures

We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given.Comment: 22 pages, plus an Addendu

Feynman Diagrams to Three Loops in Three Dimensional Field Theory

The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar $\lambda\phi^4$ theory.Comment: 29 pages, latex, 7 figures drawn with feynMF package, added an erratum file published in NPB513(1998)761 (single copies can be downloaded and printed for the reader's personal research and study, see http://www.elsevier.com/locate/nuclphysb

The behavioral approach to systems and modeling

An introduction to behavioral system theory, and a brief review of the content of the Special Issue are given