Fields,observables and gauge transformations II

We wish to study the construction of charge-carrying fields given the representation of the observable algebra in the sector of states of zero charge. It is shown that the set of those covariant sectors which can be obtained from the vacuum sector by acting with localized automorphisms has the structure of a discrete Abelian group. An algebra of fields can be defined on the Hilbert space of a representation of the observable algebra which contains each of the above sectors exactly once. The dual group of acts as a gauge group on in such a way that is the gauge invariant part of is made up of Bose and Fermi fields and is determined uniquely by the commutation relations between spacelike separated fields.     

Gas-phase thermal isomerization of hexachlorocyclopropane

The gas-phase thermal isomerization of hexachlorocyclopropane to hexachloropropene at 208–283°C is first order and unaffected by changes in the surface-to-volume ratio or by the addition of iodine, tetrachloroethylene, and oxygen. The first-order rate constants fit the Arrhenius equation The reaction was interpreted as an unimolecular process taking place with chlorine atom migration. A comparison of the reactivities of several chlorocyclopropanes is made.     

The exponential interaction in Rn

We prove that the Schwinger functions for the ultraviolet cut-off exponential interaction with euclidean measure exp {;?λ∫Λ:e^αξk(x):dx} dμ₀(ξ/ ∫ exp{?λ∫Λ:e^αξk(x):dx} dμ₀(ξ), λ > 0, converge as the ultraviolet cut-off is removed. The limits are the free Schwinger functions in the case of space-time dimension n ? 3. In the case n = 2 this holds for |α| sufficiently big, whereas for |α| < 2 √π, one has the well-known nontrivial Schwinger functions of the exponential interaction.     

Equazioni ellittiche non variazionali a coefficienti continui

Riassunto Si considera un'equazione ellittica non variazionale a_aD^au=f a coefficienti continui in un apertogW di ℝⁿ e si dimostrano certe proprietà locali delle soluzioni forti dell'equazione medesima nell'ipotesi che f appartenga allo spazio di Morrey L ^2,λ(Ω) o allo spazio di John-Nirenberg ℰ(Ω). Analoga indagine è svolta supponendoΩ=ℝ ₊ ⁿ e supponendo che u verifichi sull'iperpiano x_n=0 condizioni di Dirichlet omogenee. Ricerca svolta nell'ambito dei Contratti di Ricerca del Comitato per la Matematica del C.N.R. Entrata in Redazione il 17 febbraio 1970.     

Absorption line shape of two coupled oscillators decaying in the same bath

In this paper the linear response theory approximation is used to calculate the electromagnetic energy absorption coefficient of two coupled oscillators decaying in the same medium. The model seems to be suitable for the treatment of the infrared spectroscopy of certain isolated molecules trapped in a rare gas crystal.     

The failure of reactivity indices as quantitative measures of the susceptibility of heterocyclic compounds to electrophilic substitution

The effects of poly-substitution and heteroatom substitution in benzene on the hydrogen-exchange rate are so different to the effects of the same substitutions on the nitration rate as to preclude any universal index of the susceptibility of an individual ring position towards electrophilic substitution.     

Diolefin rhodium(I) complexes with tropolone and related ligands

Summary Rhodium(I) tropolonate and salicylaldehydate complexes of the general formula Rh(A)(diolefin) (A = tropolonate, -iso-propyltropolonate, -methyltropolonate and salicylaldehydate; diolefin = 1,5-cyclooctadiene, 2,5-norbornadiene and tetrafluorobenzobarrelene) have been prepared by several routes. The ability of Rh(trop)(COD) to function as an intermediate for the synthesis of other neutral and cationic rhodium(I) complexes has been studied and its hydroformylation activity has been explored briefly.     

Micelles and reverse micelles in the nickel bis(2-ethylhexyl) sulfosuccinate/water/isooctane microemulsion

The ternary system Ni(2+)(AOT)(2) (nickel 2-bis[2-ethylhexyl] sulfosuccinate)/water/isooctane presents w/o and o/w microemulsions with a Winsor progression (2Phi-3Phi-2Phi), without the addition of salt; the "fish diagram" was obtained for alpha=0.5 and gamma=0.02-0.22. Using static and dynamic light scattering the micellar size, the ratio of water to surfactant, and the density of micelles for this system were estimated. In addition, the mean interfacial curvature as a function of temperature was obtained.     

Insights into CO/styrene copolymerization by using Pd(II) catalysts containing modular pyridine-imidazoline ligands

Continuing our studies into the effect that N-N' ligands have on CO/styrene copolymerization, we prepared new C(1)-symmetrical pyridine-imidazoline ligands with 4',5'-cis stereochemistry in the imidazoline ring (5) and 4',5'-trans stereochemistry (6-10) and compared them with our previously reported ligands (1-4). Their coordination to neutral methylpalladium(II) (5 a-10 a) and cationic complexes (5 b-10 b), investigated in solution by NMR spectroscopy, indicates that both the electronic and steric properties of the imidazolines determine the stereochemistry of the palladium complexes. The crystal structures of two neutral palladium precursors [Pd(Me)(2-n)Cl(n)(N-N')] (n=1 for 8 a; n=2 for 9 a') show that the Pd-N coordination distances and the geometrical distortions in the imidazoline ring depend on the electronic nature of the substituents in the imidazoline fragment. Density functional calculations performed on selected neutral and cationic palladium complexes compare well with NMR and X-ray data. The calculations also account for the formation of only one or two stereoisomers of the cationic complexes. The performance of the cationic complexes as catalyst precursors in CO/4-tert-butylstyrene copolymerization under mild pressures and temperatures was analyzed in terms of the productivity and degree of stereoregularity of the polyketones obtained. Insertion of CO into the Pd-Me bond, which was monitored by multinuclear NMR spectroscopy, shows that the N ligand influences the stereochemistry of the acyl species formed.