Partial Ordering of Gauge Orbit Types for SU(n)-Gauge Theories

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space-time, derived earlier, is used. It is shown that, on the level of these cohomology elements, the partial ordering relation is characterized by a system of algebraic equations. Moreover, operations to generate direct successors and direct predecessors are formulated. The latter allow to successively reconstruct the set of orbit types, starting from the principal type.Comment: 35 pages, LaTe

Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for \complex \mbox{\LARGE P}^n

Based on a closed formula for a star product of Wick type on \CP^n, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the uniformly dense subspace of representative functions with respect to the canonical action of the unitary group) that consists of {\em converging} power series in the formal parameter, thereby giving an elementary algebraic proof of a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this subalgebra the formal parameter can be substituted by a real number $\alpha$: the resulting associative algebras are infinite-dimensional except for the case $\alpha=1/K$, $K$ a positive integer, where they turn out to be isomorphic to the finite-dimensional algebra of linear operators in the $K$th energy eigenspace of an isotropic harmonic oscillator with $n+1$ degrees of freedom. Other examples like the $2n$-torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font

Anomalous magneto-oscillations and spin precession

A semiclassical analysis based on concepts developed in quantum chaos reveals that anomalous magneto-oscillations in quasi two-dimensional systems with spin-orbit interaction reflect the non-adiabatic spin precession of a classical spin vector along the cyclotron orbits.Comment: 4 pages, 2 figure

A Boolean Gene Regulatory Model of heterosis and speciation

Modelling genetic phenomena affecting biological traits is important for the development of agriculture as it allows breeders to predict the potential of breeding for certain traits. One such phenomenon is heterosis or hybrid vigor: crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance. Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict. We have taken a computational approach to studying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework. Fitness is measured as the ability of a network to respond to external inputs in a pre-defined way. Our model reproduced common experimental observations on heterosis using only biologically justified parameters. Hybrid vigor was observed and its extent was seen to increase as parental populations diverged, up until a point of sudden collapse of hybrid fitness. We also reproduce, for the first time in a model, the fact that hybrid vigor cannot easily be fixed by within a breeding line, currently an important limitation of the use of hybrid crops. The simulation allowed us to study the effects of three standard models for the genetic basis of heterosis and the level of detail in our model allows us to suggest possible warning signs of the impending collapse of hybrid vigor in breeding. In addition, the simulation provides a framework that can be extended to study other aspects of heterosis and alternative evolutionary scenarios.Comment: See online version for supplementary materia

Elution study of acrylic monomers from orthodontic materials using high performance liquid chromatography (HPLC)

Purpose: Main goal of the study was the identification and quantitative analysis of monomer elution from materials commonly used in fixed orthodontic therapy. Studies have shown severe health effects of monomers including cytotoxic, allergenic or mutagenic potential and endocrine changes. This in vitro study focusses primarily on five resins which are usually processed intraorally and remain in the oral cavity long-term. Methods: We tested the elution of monomers from specimens (7.5 mm x 1.5 mm) immersed in artificial saliva at body temperature (37 degrees C) for 30 min to 5 weeks. The used method is in accordance with DIN EN ISO 10993-13. The five tested materials were BrackFix (R) (Voco GmbH, Cuxhaven, Germany), Triad (R) Gel (DeguDent GmbH, Hanau, Germany), and Transbond (TM) XT, LR and Plus (3M Unitek, Monrovia, CA, USA). All aliquots were analyzed using high performance liquid chromatography (HPLC). Data were statistically analyzed. Results: All five analyzed materials eluted substances over a period of 5 weeks. Identified substances included bisphenol A (BPA), triethylene glycol dimethacrylate (TEGDMA) and urethane dimethacrylate (UDMA). BPA eluted from Transbond (TM) Plus, XT, LR and BrackFix (R). The cumulated mean values after 35 days ranged from 16.04 to 64.83 ppm, depending on the material. TEGDMA eluted with a mean of 688.61 ppm from Transbond (TM) LR. UDMA with a mean of 1682.00 ppm from Triad (R) Gel. For each material the highest concentrations of all these substances were found in the first elution period. Other substances that were not equivocally identified or of low concentration also eluted. Conclusion: Using the described method, it is possible to qualitatively and quantitatively determine the in vitro elution of monomers from orthodontic materials. The concentrations of the substances identified were below the current maximum recommended intake. However, a cumulative effect and low-dose effects should be considered for both patients and dental professionals, especially for young patients. Measures to reduce exposure patients and practitioners are suggested

Phase Space Reduction for Star-Products: An Explicit Construction for CP^n

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on $C^{n+1} \setminus \{ 0 \}$, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on \CP^n which can easily transferred to the domain $SU(n+1)/S(U(1)\times U(n))$.Comment: LaTeX, 17 page

Symplectic Dirac-K\"ahler Fields

For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-K\"ahler fields can be defined on the classical phase-space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.Comment: 86 pages, late

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2