Concerning the reactivity of dioxiranes. Observations fromexperiments and theory

The challenging hypothesis of a “biphilic” (i.e., electrophilic vs nucleophilic) character for dioxirane reactivity, which envisages that electron-poor alkenes are attacked by dioxiranes in a nucleophilic fashion, could not be sustained experimentally. Rate data, which estimate Hammett “rho” values for the epoxidation of 3- or 4-substituted cinnamonitriles XâPhsCHdCHsCN, unequivocally allow one to establish that dioxiranes epoxidize electrophilically even alkenes carrying electron-withdrawing groups. The greater propensity of methyl(trifluoromethyl)dioxirane TFDO (1b) to act as an electrophilic oxidant with respect to dimethyldioxirane DDO (1a) parallels the cathode reduction potentials for the two dioxiranes, as measured by cyclic voltammetry. A simple FMO approach for alkene epoxidation is helpful to conceive a likely rationale for the greater oxidizing power of TFDO as compared to DDO

Some Conjectures on the Limit of Infinite Higgs Mass

We consider a possible field theory candidate for the electroweak SU(2) x U(1) model where the limit of infinitely sharp Higgs potential is performed. We show that it is possible to formulate such a limit as a Stueckelberg massive non abelian gauge theory.Comment: One reference added. Final version to appear in the journa

Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs

We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p^2=0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the theory is unitary. The proof of unitarity is given both in a form that allows a direct transcription in terms of Feynman amplitudes (cutting rules) and in the operatorial form. The same arguments and conclusions apply verbatim to the case of non-abelian gauge theories where the mass of the vector meson is generated via Higgs mechanism. To the best of our knowledge, there is no mention in the literature on the necessary condition implied by physical unitarity.Comment: References added. 22 pages. Final version to appear in the journa

Endowing the Nonlinear Sigma Model with a Flat Connection Structure: a Way to Renormalization

We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term a` la Stueckelberg. However the paper is limited to the case where only the flat connection is present (no field strength term). The perturbative solution is constructed by using only the functional equations and by expanding in the number of loops. In particular we do not use a perturbative approach based on the path integral or on a canonical quantization. It is shown that there is no solution with trivial S-matrix. Then the model is embedded in a nonlinear sigma model. The solution is constructed by exploiting a natural hierarchy in the functional equations given by the number of insertions of the flat connection and of the constrained component of the sigma field. The amplitudes with the sigma field are simply derived from those of the flat connection and of the constraint component. Unitarity is enforced by hand by using Feynman rules. We demonstrate the remarkable fact that in generic dimensions the naive Feynman rules yield amplitudes that satisfy the functional equations. This allows a dimensional renormalization of the theory in D=4 by recursive subtractions of the poles in the Laurent expansion. Thus one gets a finite theory depending only on two parameters. The novelty of the paper is the use of the functional equation associated to the local left multiplication introduced by Faddeev and Slavnov, here improved by adding the external source coupled to the constrained component. It gives a powerful tool to renormalize the nonlinear sigma model.Comment: 42 pages, 7 figures, Latex; improved presentation of the subtraction procedur

Oxyfunctionalization of Nonnatural Targets by Dioxiranes. Selective Oxidation of Centropolyindans

Kuck D, Schuster A, Fusco C, Fiorentino M, Curci R. Oxyfunctionalization of Nonnatural Targets by Dioxiranes. Selective Oxidation of Centropolyindans. Journal of the American Chemical Society. 1994;116(6):2375-2381.The oxyfunctionalization of four centropolyindans, i.e., triptindan (2), 1,1'-(o-phenylene)-2,2'-spirobiindan (3), 10-methyltribenzoquinacene (4), and fenestrindan (5) at the benzylic and/or benzhydrylic C-H bonds of their rigid polycyclic framework has been achieved using dimethyldioxirane 1a and methyl(trifluoromethyl)dioxirane 1b. The latter reagent was found to be considerably more effective than 1a, allowing both partial and complete oxyfunctionalization of the substrates examined. The rigidity of the polycyclic framework and steric factors in 2-5 seem to moderate the reactivity and selectivity of the dioxiranes with respect to O-insertion into benzhydrylic vs benzylic C-H bonds; for instance in the oxyfunctionalization of the angular centrotriindan 3, the secondary benzylic alcohol 12 and the corresponding ketone 10 are obtained, along with the isomeric tertiary alcohol 11. The potentiality of 1b in effecting multiple oxygen insertion into C-H bonds under quite mild conditions was demonstrated by the remarkable high yield 4-fold hydroxylation of fenestrindan (5) at the bridgehead positions. The results are interpreted in terms of an essentially concerted O-insertion by the dioxirane into the C-H bonds encompassed in the rigid framework of the substrates. Adoption of an FMO model, which envisages dioxirane attack along the O-O bond axis toward the carbon atom of the given C-H bonds, provides a rationale for the reactivities and selectivities recorded