Browsing by Author "Duetsch, Michael"

A wide range of cyclopenta[b]pyrans 4 has been synthesized in a one-pot reaction by treatment of different 2-donorsubstituted ethenylcarbene-chromium complexes 2 with alkynes in THF in moderate to excellent yields (41-90% for 14 out of 25 examples). The starting materials 2 are readily available in good to excellent yields (76-99% for 25 out of 36 examples) by Michael addition of amines, alcohols and thiols, respectively, to the corresponding alkynylcarbenechromium complexes 1. Due to their 10 pi-electrons in a cross-conjugated bicyclic system, cyclopenta[b]pyrans have been termed pseudoazulenes, as they indeed have similar UV/Vis-spectroscopic properties.

The cocyclization reaction of pentacarbonyl(beta -amino-1-ethoxyalkenylidene)chromium complexes 1 with alkynes has been studied with respect to the effects of substituents, solvents, ligand additives, and reagent concentrations upon the product distribution. This reaction proceeds either as a formal [2 + 2 + 1] cycloaddition to give 5-(1'-dialkylaminoalkylidene)-4-ethoxycycloopent-2-enous 8 or a formal [3 + 2] cycloaddition to give 5-dialkylamino-3-ethoxy-1,3-cyclopentadienes 9. A working hypothesis for the mechanism of this reaction is proposed on the basis of that previously determined for the Dotz reaction. The effects of the aforementioned parameters upon the product distribution of this current reaction are explained in terms of this model. A pronounced ligand-induced allochemical effect has been observed. Conditions for the selective preparation of both classes of cycloadducts 8 and 9 have been determined.

The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling constant(s) and the masses. Since, under the renormalization group (RG) flow, different interaction terms get different loop-corrections, it is uncertain whether these functions remain fixed under this flow. We investigate this question for the U(1)-Higgs-model to 1-loop order in the framework of Epstein-Glaser renormalization. Our main result reads: choosing the renormalization mass scale(s) in a way corresponding to the minimal subtraction scheme, the geometrical interpretation as a spontaneously broken gauge theory gets lost under the RG-flow. This holds also for the clearly stronger property of BRST-invariance of the Lagrangian. On the other hand, we prove that physical consistency, which is a weak form of BRST-invariance of the time-ordered products, is maintained under the RG-flow.

Out of conviction or expediency, some current research programs (Kostelecky (2008) [1], Kostelecky and Russell (2011) [2], Ferrero and Altschul (2011) [3], Anselmi (2009) [4]) take for granted that "PCT violation implies violation of Lorentz invariance". We point out that this claim (Greenberg (2002) [15]) is still on somewhat shaky ground. In fact, for many years there has been no strengthening of the evidence in this direction. However, using causal perturbation theory, we prove here that when starting with a local PCT-invariant interaction, PCT symmetry can be maintained in the process of renormalization. (c) 2012 Elsevier B.V. All rights reserved.

A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low-dimensional theories and of non-polynomial interactions. We discuss the connection between the Stuckelberg-Petermann renormalization group which describes the freedom in the perturbative construction with the Wilsonian idea of theories at different scales. In particular, we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method. We also show that the renormalization group in the sense of Gell-Mann-Low (which characterizes the behaviour of the theory under the change of all scales) is a one-parametric subfamily of the Stuckelberg-Petermann group and that this subfamily is in general only a cocycle. Since the algebraic structure of the Stuckelberg-Petermann group does not depend on global quantities, this group can be formulated in the (algebraic) adiabatic limit without meeting any infrared divergencies. In particular we derive an algebraic version of the Callan-Symanzik equation and define the beta-function in a state independent way.

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski space-time is viewed as the boundary limit of a quantum field phi on d + 1-dimensional Anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the one-loop "fish diagram" on AdS(4) by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi(2) with bulk interaction kappa phi(4).

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.