Affine lie algebras in massive field theory and form factors from vertex operators

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions by investigating theq1 limit of theq-deformed affine symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebrasplit into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector, and level 0 in the periodic sector. The space of fields in the anti-periodic sector can be organized using level-1 highest weight representations if one supplements the algebra with the usual local integrals of motion. Introducing a particle-field duality leads to a new way of computing form-factors in radial quantization. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. Form-factors are computed as vacuum expectation values of vertex operators in momentum space.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 430–441, March, 1994.     

Nonlocal forces of inertia in cosmology

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic universe. This matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant.     

Formal orthogonal polynomials revisited. Applications

From some results concerning the formal orthogonal polynomials, already proved in [5], we develop new properties of generalized adjacent polynomials which correspond to a change in the weight function. A new structure of the singular blocks is given. These results have a direct application to Lanczos methods, theG and -algorithms.     

Synthesis, Structural Characterization, and Oxidation-Reduction Behavior of the gamma-Isomer of the Dodecatungstosilicate Anion

The reaction of tungstate ions with the gamma-10-tungstosilicate in mixed water-ethanol (v/v) yields the corresponding isomer of the 12-tungstosilicate isolated as its tetrabutylammonium salt. It was characterized by means of (183)W NMR, infrared, Raman, and UV spectroscopies and was identified with the isomer resulting from the Keggin structure (alpha-isomer) by rotation of two tritungstic groups by pi/3. Cyclic voltammetry shows that the reducibility increases in the sequence alpha-beta-gamma as the number of rotated tritungstic groups. Whereas the gamma-12-tungstosilicate anion is unstable in pure aqueous solution whatever the pH value, it is stable in mixed aqueous-organic or pure organic solvents, even at boiling temperatures. In contrast, the two- and four-electron-reduced blue species are stable in aqueous media but not the one-electron-reduced blue. Study of the (183)W NMR spectrum of the two-electron-reduced species showed that the two spin-paired electrons are delocalized on all the W atoms on the NMR time scale but have a larger residency time on one group of four atoms.     

Novel Cleavage of Propargylamines by Reaction with Organolithium Compounds

Treatment of secondary aliphatic 2-bromoallylamines with an excess of an organolithium compound led to saturated amines in which the organic group of the organolithium compound is incorporated at the alpha carbon. On the other hand, the successive reaction of the former amines with BuLi and t-BuLi between -80 degrees C and rt gave 1,3-diamines or hexahydropyrimidines depending on the reaction time. The formation of these unexpected products involves initial generation of lithium propargylamides, which subsequently undergo cleavage of the C propargylic-C acetylenic bond induced by the organolithium present in each case in the reaction medium. A mechanism which takes into account all the different reaction products has been proposed and additionally supported by successful trapping of dilithium acetylide.