AQFT from <Emphasis Type="Italic">n</Emphasis>-Functorial QFT

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to “extended” functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra “of observables”, the latter uses n-functors which assign to each patch a “propagator of states”.In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor (“parallel surface transport”) naturally yields a local net, whose locality derives from the 2-categorical exchange law, and which is covariant if the 2-functor is equivariant. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schrödinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general Lorentzian structure, bare lightcone structure and higher dimensions. It does not, however, by itself imply anything about the existence of a vacuum state or about positive energy representations.     

John Napiers Trigonometrie – ein Blick zurück

Zusammenfassung  Dieser Artikel gibt einen überblick über Napiers Beitr?ge zur sph?rischen Trigonometrie, wobei die dafür notwendigen sachlichen und historischen Grundlagen weitgehend bereitgestellt werden. Da diese Beitr?ge in der Literatur trotz ihrer erheblichen Bedeutung ganz im Schatten von Napiers Logarithmen stehen, erscheint eine solche Zusammenschau gerechtfertigt. Auch kommen einige neue oder kaum bekannte Einzelheiten zur Sprache. Mathematics subject classification (2000)  01A45 · 51-03     

Strong cooperativeness in the mononuclear iron(II) derivative exhibiting an abrupt spin transition above 400 K

The spin crossover system, [Fe(bzimpy)(2)](ClO(4))(2).0.25H(2)O, was reinvestigated above room temperature (bzimpy = 2,6-bis(benzimidazol-2-yl)pyridine). The system exhibits an abrupt low-spin to high-spin transition at T(c) = 403 K. Liberation of a fractional amount of water does not affect the spin crossover: the system is perfectly reversible with a hysteresis width of DeltaT = 12 K. The existence of the hysteresis at such high temperature determines that the lowest limit of the solid-state cooperativity parameter is J/k > 403 K despite long iron(II) separations (10 A). The high cooperativeness has been assigned to a perfect pi-stacking of the benzimidazole rings in the crystal lattice at a distance as short as 3.6 A. Variable-temperature IR data and the heat capacity measurements match well the magnetic data. The thermodynamic properties are DeltaH = 17 kJ mol(-)(1), DeltaS = 43 J K(-)(1) mol(-)(1), so that the entropy of the spin transition shows a considerable contribution from the molecular vibrations. A theoretical model has been applied in fitting the magnetic data along the whole hysteresis path. A statistical distribution of the cooperativity parameter led to the feature that angled walls of the hysteresis loop are well reproduced.     

2,4‐Dioxa‐7‐aza‐, 2,4‐Dioxa‐8‐aza‐, and 2,4‐Dioxa‐9‐aza‐3‐phosphadecalins as Rigid Acetylcholine Mimetics: Syntheses and Characterization

Phosphorylation of suitable piperidine precursors yielded a series of novel decalin‐type O,N,P‐heterocycles. The title compounds, P(3)‐axially and P(3)‐equatorially X‐substituted, cis‐ and trans‐configurated 2,4‐dioxa‐7‐aza‐, 2,4‐dioxa‐8‐aza‐, and 2,4‐dioxa‐9‐aza‐3‐phosphabicyclo[4.4.0]decane 3‐oxides (X=Cl, F, 4‐nitrophenoxy, and 2,4‐dinitrophenoxy), are configuratively fixed and conformationally constrained P‐analogues of acetylcholine and as such represent acetylcholine (7‐aza and 9‐aza isomers) or γ‐homo‐acetylcholine mimetics (8‐aza isomers). Being irreversible inhibitors of acetylcholinesterase (AChE), the compounds are considered to be suitable probes for the investigation of the stereochemical course of the inhibition reaction by ³¹P‐NMR spectroscopy. Moreover, the design of these mimetics will enable studies of molecular interactions with AChE, in particular, the recognition conformation of acetylcholine.