Inhomogeneous quantum groups IGL_{q,r}(N): Universal enveloping algebra and differential calculus

A review of the multiparametric linear quantum group GL_qr(N), its real forms, its dual algebra U(gl_qr(N)) and its bicovariant differential calculus is given in the first part of the paper. We then construct the (multiparametric) linear inhomogeneous quantum group IGL_qr(N) as a projection from GL_qr(N+1), or equivalently, as a quotient of GL_qr(N+1) with respect to a suitable Hopf algebra ideal. A bicovariant differential calculus on IGL_qr(N) is explicitly obtained as a projection from the one on GL_qr(N+1). Our procedure unifies in a single structure the quantum plane coordinates and the q-group matrix elements T^a_b, and allows to deduce without effort the differential calculus on the q-plane IGL_qr(N) / GL_qr(N). The general theory is illustrated on the example of IGL_qr(2).Comment: 38 page

Yang-Mills and Born-Infeld actions on finite group spaces

Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F\wedge *F . This technique is extended to obtain a discrete version of the Born-Infeld action.Comment: Talk presented at GROUP24, Paris, July 2002. LaTeX, 4 pages, IOP style

On localization effects in underdoped cuprates

We comment on transport experiments in underdoped LaSrCuO in the non-superconducting phase. The temperature dependence of the resistance strongly resembles what is expected from standard localization theory. However this theory fails, when comparing with experiments in more detail.Comment: 8 pages, to be published in J. of Superconductivit

Stellar Evolutionary Models for Magellanic Clouds

We supplement current evolutionary computations concerning Magellanic Cloud stars by exploring the evolutionary behavior of canonical stellar models (i.e.,with inefficient core overshooting) with metallicities suitable for stars in the Clouds. After discussing the adequacy of the adopted evolutionary scenario, we present evolutionary sequences as computed following a selected sample of stellar models in the mass range 0.8-8 Mo from the Main Sequence till the C ignition or the onset of thermal pulses in the advanced Asymptotic Giant Branch phase. On this basis, cluster isochrones covering the range of ages from 100 Myr to 15 Gyr are presented and discussed. To allow a comparison with evolutionary investigations appeared in the recent literature, we computed additional sets of models which take into account moderate core overshooting during the H burning phase, discussing the comparison in terms of current uncertainties in the stellar evolutionary models. Selected predictions constraining the cluster ages are finally discussed, presenting a calibration of the difference in magnitude between the luminous MS termination and the He burning giants in terms of cluster age. Both evolutionary tracks and isochrones have been made available at the node http://gipsy.cjb.net as a first step of a planned ``Pisa Evolutionary Library''.Comment: 11 pages, 9 eps figures, A&A accepted, evolutionary tracks and isochrones available at http://gipsy.cjb.net at the link ``Pisa Evolutionary Library'

Super Quantum Mechanics in the Integral Form Formalism

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincar\'e duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.Comment: 41 pages, no figures. Use birkjour.cls. Minor misprints, moved appendix A and B in the main text. Version to be published in Annales H. Poincar\'

The Geometry of Supermanifolds and New Supersymmetric Actions

We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and superforms in a new way which can be easily generalised to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.Comment: LateX2e, 51 pages. Corrected some further misprint

R-Matrix Formulation of the Quantum Inhomogeneous Groups Iso_qr(N) and Isp_qr(N)

The quantum commutations $RTT=TTR$ and the orthogonal (symplectic) conditions for the inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type are found in terms of the $R$-matrix of $B_{n+1},C_{n+1},D_{n+1}$. A consistent Hopf structure on these inhomogeneous $q$-groups is constructed by means of a projection from $B_{n+1},C_{n+1},D_{n+1}$. Real forms are discussed: in particular we obtain the $q$-groups $ISO_{q,r}(n+1,n-1)$, including the quantum Poincar\'e group.Comment: 14 pages, latex, no figure

Hot Flashers and He Dwarfs in Galactic Globulars

We revisit the evolutionary scenario for Hot Flasher low-mass structures, where mass loss delays the He flash till the initial phases of their White Dwarf cooling sequence. Our aim has been to test the theoretical results vis-a-vis different assumptions about the efficiency of mass loss. To this purpose, we present evolutionary models covering a fine grid of masses, as obtained assuming a single episode of mass loss in a Red Giant model of 0.86 Mo with Z=0.0015. We find a reasonable agreement with previous evolutionary investigations, showing that for the given metallicity late Hot Flashers are predicted to cover the mass range M=0.4975 to M= 0.4845 Mo, all models igniting the He-flash with a mass of the H-rich envelope as given by about Me=0.00050. The ignition mechanism is discussed in some details, showing the occurrence of a bifurcation in the evolutionary history of stellar structures at the lower mass limit for He ignition. Below such a critical mass, the structures miss the He ignition, cooling down as a Hot Flasher-Manque' He White Dwarfs We predict that these structures will cool down, reaching the luminosity logL/Lo=-1 in a time at the least five times longer than the corresponding cooling time of a normal CO White Dwarf. On very general grounds, one expects that old stellar clusters with a sizeable population of Hot Flasher should likely produce at least a similar amount of slow-cooling He White Dwarfs. According to this result, in a cluster where 20% of Red Giants escape the He burning phase, one expects roughly twice as White Dwarfs than in a normal cluster where all Red Giants undergo their He flas