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

Cech and de Rham Cohomology of Integral Forms

We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory of integration in supermanifolds. One can define the integral forms introducing a new sheaf containing, among other objects, the new basic forms delta(dtheta) where the symbol delta has the usual formal properties of Dirac's delta distribution and acts on functions and forms as a Dirac measure. They satisfy in addition some new relations on the sheaf. It turns out that the enlarged sheaf of integral and "ordinary" superforms contains also forms of "negative degree" and, moreover, due to the additional relations introduced, its cohomology is, in a non trivial way, different from the usual superform cohomology.Comment: 20 pages, LaTeX, we expanded the introduction, we add a complete analysis of the cohomology and we derive a new duality between cohomology group

Balanced superprojective varieties

We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson\u2019s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context

Inclusion of the phytoalexin trans-resveratrol in native cyclodextrins: a thermal, spectroscopic, and X-ray structural study

The aim of the study was to determine the feasibility of complexation between the antioxidant trans-resveratrol (RSV) and underivatized cyclodextrins (CDs) using a variety of preparative methods, including physical mixing, kneading, microwave irradiation, co-evaporation, and co-precipitation techniques. Products were characterized using differential scanning calorimetry (DSC), simultaneous thermogravimetric/DSC analysis (TGA/DSC), Fourier transform infrared (FT-IR) spectroscopy, and powder X-ray diffraction (PXRD). With alfa-CD and RSV, sample amorphization was revealed by PXRD and FT-IR, but no definitive inclusion complexation was evident. Similar results were obtained in attempts to complex RSV with beta-CD. However, complex formation between gamma-CD and RSV was evident from observation of an endo-/exothermic effect appearing in the DSC trace of the product from kneading and was further corroborated by FT-IR and PXRD methods. The latter technique indicated complexation unequivocally as the diffraction peak profile for the product matched that for known isostructural gamma-CD complexes. Single crystal X-ray analysis followed, confirming the predicted complex between gamma-CD and RSV. A combination of 1H NMR and TGA data yielded the complex formula (g-CD)3(RSV)4(H2O)62. However, severe disorder of the RSV molecules prevented their modeling. In contrast, our previous studies of the inclusion of RSV in methylated CDs yielded crystals with only minor guest disorder