Linear bosonic quantum field theories arising from causal variational principles

We describe discrete symmetries of two-dimensional Yang–Mills theory with gauge group G associated with outer automorphisms of G, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted G-bundles and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted G-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang–Mills theory but with gauge group given by an extension of G by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang–Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.

     

A variational principle in discrete space–time: existence of minimizers

We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations.     

Hydrolysis of the uranyl ion in sodium nitrate medium

Studies on Nickel Oxide Mixed Catalysts. VIII. Catalytic Properties of NiO? Al₂O₃/SiO₂ Catalysts Catalytic properties of NiO? Al₂O₃/SiO₂ catalysts prepared by precipitation-deposition and impregnation have been investigated in dimerization of ethene and isomerization of but-1-ene. It was found that the catalytic activity is mainly determined by the interaction between the catalyst components where a X-ray amorphous nickel alumolayersilicate is formed. The dimerization of ethene proceeds by participation of coordinatively unsaturated nickel ions with aluminum ions in the neighbourhood. The catalytic activity in the isomerization of but-1-ene depends on the surface acidic properties of the catalyst.     

Banach manifold structure and infinite-dimensional analysis for causal fermion systems

Annals of Global Analysis and Geometry - A mathematical framework is developed for the analysis of causal fermion systems in the infinite-dimensional setting. It is shown that the regular spacetime...     

RP-HPLC determination of lipophilicity in series of quinoline derivatives

In the present paper we describe results on the synthesis and lipophilicity determination of a series of biologically active compounds based on their heterocyclic structure. For synthesis of styrylquinoline-based compounds we applied microwave irradiation and solid phase techniques. The correlation between RP-HPLC retention parameter log k (the logarithm of retention factor k) and log P data calculated in various ways is discussed, as well as, the relationships between the lipophilicity and the chemical structure of the studied compounds.      

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which satisfies the dominant energy condition and is time-periodic, thus running through an infinite number of contraction and expansion cycles.     

Chemical and structural order in silicon oxynitrides by methods of surface physics

A large number of thin amorphous layers of SiO_xN_y and several (crystalline) reference compounds (SiO₂, Si₃N₄, Si₂N₂O) are studied. Although XANES and SEXAFS are well sulted to derive structural and chemical order, for these compounds many problems remain to be solved. We show how core level spectra (XPS, AES) can be used to gain such information (e.g. random bonding structure, N coordination, oxidation behaviour).     

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou’s result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator. Research supported in part by the Deutsche Forschungsgemeinschaft. Research supported by NSERC grant # RGPIN 105490-2004. Research supported in part by the Humboldt Foundation and the National Science Foundation, Grant No. DMS-0603754. Research supported in part by the NSF, Grant No. 33-585-7510-2-30.