An Algebraic Version of Haag’s Theorem

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with bases on a fixed space-like hyperplane completely determines an algebraic QFT model. More precisely, if for two models there is a unitary connecting all of these algebras, then — without assuming that this unitary also connects their respective vacuum states or spacetime symmetry representations — it follows that the two models are equivalent. This result might be viewed as an algebraic version of the celebrated theorem of Rudolf Haag about problems regarding the so-called “interaction-picture” in QFT. Original motivation of the author for finding such an algebraic version came from conformal chiral QFT. Both the chiral case as well as a related conjecture about standard half-sided modular inclusions will be also discussed.     

Photoreduction of carbon dioxide to carbon monoxide with hydrogen catalyzed by a rhenium(i) phenanthroline-polyoxometalate hybrid complex

A phenanthroline ligand decorated at the 5,6-position with a 15-crown-5 ether was used to prepare a metalorganic-polyoxometalate hybrid complex Re(I)(L)(CO)(3)CH(3)CN-MHPW(12)O(40) (L = 15-crown-5-phenanthroline, M = Na(+), H(3)O(+)). X-ray diffraction, (1)H and (13)C NMR, ESI-MS, IR, and elemental analysis were used to characterize this complex. In the presence of Pt/C, the polyoxometalate moiety in Re(I)(L)(CO)(3)CH(3)CN-MHPW(12)O(40) can oxidize H(2) to two protons and two electrons which in the presence of visible light can catalyze the photoreduction of CO(2) to CO with H(2) as the reducing agent instead of the universally used amines as sacrificial reducing agents. An EPR spectrum of a stable intermediate species under reaction conditions shows characteristics of a PW(V)W(VI)(11)O(40) and a Re(0) species with a tentative assignment of the intermediate as Re(0)(L)(CO)(3)(S)-MH(3)PW(V)W(VI)(11)O(40).     

Three-dimensional H spectroscopic imaging of cerebral metabolites in the rat using surface coils

Three dimensional metabolite maps of protonated metabolites were obtained using ¹H magnetic resonance spectroscopic imaging at 7 T. Surface coils were used to increase sensitivity and spatial resolution significantly over a volume coil two-dimensional acquisition. Adiabatic pulses were employed to provide homogeneous B₁ excitation and frequency selective refocusing over the volume of the rat brain. These techniques were employed to obtain three-dimensional spectroscopic imaging spectra from nominal voxel volumes of 9–30 μl from rat brain. The improved spatial resolution and sensitivity are also demonstrated with studies of focal ischemia in the rat.     

Poincaré Covariance of Relativistic Quantum Position

A great number of problems of relativistic position in quantum mechanics are because of the use of coordinates that are not inherent objects of spacetime, cause unnecessary complications, and can lead to misconceptions. We apply a coordinate-free approach to rule out such problems. Thus it will be clear, for example, that the Lorentz covariance of position, required usually on the analogy of Lorentz covariance of spacetime coordinates, is not well posed and we show that in a right setting the Newton–Wigner position is Poincaré covariant.     

Photoisomerization of dichlorocarbene adducts of 2,4-cyclohexadienones

Irradiation of the nπ* band of the dichlorocyclopropyl enones $\text{1}$ and $\text{7}$ resulted in ring expansion and 1,2-chlorine migration to give $\text{2}$ and $\text{8}$ respectively, whereas the dihydrogen analog $\text{11}$ gave the vinylcyclopropane-cyclopentene rearrangement product $\text{12}$.     

Construction of unique canonical coefficients for antisymmeterized geminal power states

Coefficients often defined to be canonical for a given geminal may not be unique. In this article we show by carefully examining a theorem by B. Zumino how to construct unique canonical coefficients for a geminal. This result leads to expansions of antisymmeterized geminal power states solely in terms of natural generalized spin orbitals and positive geminal occupation numbers. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004