The Minkowski and conformal superspaces

We define complex Minkowski superspace in 4 dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex Minkowski superspace. We then consider real Minkowski superspace as a suitable real form of the complex version. Our methods are group theoretic, based on the real conformal supergroup and its Lie superalgebra.Comment: AMS LaTeX, 44 page

Star Products on Coadjoint Orbits

We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.Comment: Talk given at the XXIII ICGTMP, Dubna (Russia) August 200

Notions of Infinity in Quantum Physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.Comment: 11 page

Gauged extended supergravity without cosmological constant: no-scale structure and supersymmetry breaking

We consider the interplay of duality symmetries and gauged isometries of supergravity models giving N-extended, spontaneously broken supergravity with a no-scale structure. Some examples, motivated by superstring and M-theory compactifications are described.Comment: AMS-LaTeX, 16 pages. Invited paper to appear in the review section of the IJMP

Rheological properties of biofilms: steady and transient shear flow modeling

Premi al millor poster en la 7th Internacional Conference on Biotechniques for Air Pollution Control and BioenergyPeer ReviewedAward-winningPostprint (published version

On the deformation quantization of affine algebraic varieties

We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space

Integration of massive states as contractions of non linear σ\sigma-models

We consider the contraction of some non linear sigma models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N=1 and N=2 theories, as they appear in certain low energy effective supergravity actions with mass deformations. The contraction procedure is shown to describe the integrating out of massive modes in the presence of interactions, as it happens in many supergravity models after spontaneous supersymmetry breaking.Comment: AMS-LaTeX, 33 page

Scherk-Schwarz Reduction of D=5 Special and Quaternionic Geometry

We give the N=2 gauged supergravity interpretation of a generic D=4, N=2 theory as it comes from generalized Scherk-Schwarz reduction of D=5, N=2 (ungauged) supergravity. We focus on the geometric aspects of the D=4 data such as the general form of the scalar potential and masses in terms of the gauging of a ``flat group''. Higgs and super-Higgs mechanism are discussed in some detail.Comment: final version to be published on Class.Quant.Gra