On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Maximal sublattices and Frattini sublattices of bounded lattices

We investigate the number and size of the maximal sublattices of a finite lattice. For any positive integer k, there is a finite lattice L with more that ]L]k sublattices. On the other hand, there are arbitrary large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every bounded lattice is isomorphic to the Frattini sublattice (the intersection of all maximal sublattices) of a finite bounded lattic

Uptake and cytotoxicity of citrate-coated gold nanospheres : comparative studies on human endothelial and epithelial cells

The use of gold nanoparticles (AuNPs) for diagnostic applications and for drug and gene-delivery is currently under intensive investigation. For such applications, biocompatibility and the absence of cytotoxicity of AuNPs is essential. Although generally considered as highly biocompatible, previous in vitro studies have shown that cytotoxicity of AuNPs in certain human epithelial cells was observed. In particular, the degree of purification of AuNPs (presence of sodium citrate residues on the particles) was shown to affect the proliferation and induce cytotoxicity in these cells. To expand these studies, we have examined if the effects are related to nanoparticle size (10, 11 nm, 25 nm), to the presence of sodium citrate on the particles' surface or they are due to a varying degree of internalization of the AuNPs. Since two cell types are present in the major barriers to the outside in the human body, we have also included endothelial cells from the vasculature and blood brain barrier. Results Transmission electron microscopy demonstrates that the internalized gold nanoparticles are located within vesicles. Increased cytotoxicity was observed after exposure to AuNPs and was found to be concentration-dependent. In addition, cell viability and the proliferation of both endothelial cells decreased after exposure to gold nanoparticles, especially at high concentrations. Moreover, in contrast to the size of the particles (10 nm, 11 nm, 25 nm), the presence of sodium citrate on the nanoparticle surface appeared to enhance these effects. The effects on microvascular endothelial cells from blood vessels were slightly enhanced compared to the effects on brain-derived endothelial cells. A quantification of AuNPs within cells by ICP-AES showed that epithelial cells internalized a higher quantity of AuNPs compared to endothelial cells and that the quantity of uptake is not correlated with the amount of sodium citrate on the nanoparticles’ surface. Conclusions In conclusion the higher amount of citrate on the particle surface resulted in a higher impairment of cell viability, but did not enhance or reduce the uptake behavior in endothelial or epithelial cells. In addition, epithelial and endothelial cells exhibited different uptake behaviors for citrate-stabilized gold nanoparticles, which might be related to different interactions occurring at the nanoparticle-cell-surface interface. The different uptake in epithelial cells might explain the higher reduction of proliferation of these cells after exposure to AuNPs treatment although more detailed investigations are necessary to determine subcellular events. Nevertheless an extrinsic effect of sodium-citrate stabilized particles could not be excluded. Thus, the amount of sodium citrate should be reduced to a level on which the stability of the particles and the safety for biomedical applications are guaranteed

Measuring the cosmological lepton asymmetry through the CMB anisotropy

A large lepton asymmetry in the Universe is still a viable possibility and leads to many interesting phenomena such as gauge symmetry nonrestoration at high temperature. We show that a large lepton asymmetry changes the predicted cosmic microwave background (CMB) anisotropy and that any degeneracy in the relic neutrino sea will be measured to a precision of 1% or better when the CMB anisotropy is measured at the accuracy expected to result from the planned satellite missions MAP and Planck. In fact, the current measurements already put an upper limit on the lepton asymmetry of the Universe which is stronger than the one coming from considerations of primordial nucleosynthesis and structure formation.Comment: 4 pagex LaTex, 1 color postscript figure, uses epsf. Version submitted to PRL. (Bug in code fixed, new figure, conclusions unchanged

Dark Stars and Boosted Dark Matter Annihilation Rates

Dark Stars (DS) may constitute the first phase of stellar evolution, powered by dark matter (DM) annihilation. We will investigate here the properties of DS assuming the DM particle has the required properties to explain the excess positron and elec- tron signals in the cosmic rays detected by the PAMELA and FERMI satellites. Any possible DM interpretation of these signals requires exotic DM candidates, with an- nihilation cross sections a few orders of magnitude higher than the canonical value required for correct thermal relic abundance for Weakly Interacting Dark Matter can- didates; additionally in most models the annihilation must be preferentially to lep- tons. Secondly, we study the dependence of DS properties on the concentration pa- rameter of the initial DM density profile of the halos where the first stars are formed. We restrict our study to the DM in the star due to simple (vs. extended) adiabatic contraction and minimal (vs. extended) capture; this simple study is sufficient to illustrate dependence on the cross section and concentration parameter. Our basic results are that the final stellar properties, once the star enters the main sequence, are always roughly the same, regardless of the value of boosted annihilation or concentration parameter in the range between c=2 and c=5: stellar mass ~ 1000M\odot, luminosity ~ 10^7 L\odot, lifetime ~ 10^6 yrs (for the minimal DM models considered here; additional DM would lead to more massive dark stars). However, the lifetime, final mass, and final luminosity of the DS show some dependence on boost factor and concentration parameter as discussed in the paper.Comment: 37 pages, 11 figure

Baryogenesis from a right-handed neutrino condensate

We show that the baryon asymmetry of the Universe can be generated by a strongly coupled right handed neutrino condensate which also drives inflation. The resulting model has only a small number of parameters, which completely determine not only the baryon asymmetry of the Universe and the mass of the right handed neutrino but also the inflationary phase. This feature allows us to make predictions that will be tested by current and planned experiments. As compared to the usual approach our dynamical framework is both economical and predictive.Comment: 13 pages, 3 figures. Typos corrected and several points clarified. Results unchanged. New references adde

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio

Double Field Inflation

We present an inflationary universe model which utilizes two coupled real scalar fields. The inflation field $\phi$ experiences a first order phase transition and its potential dominates the energy density of the Universe during the inflationary epoch. This field $\phi$ is initially trapped in its metastable minimum and must tunnel through a potential barrier to reach the true vacuum. The second auxiliary field $\psi$ couples to the inflaton field and serves as a catalyst to provide an abrupt end to the inflationary epoch; i.e., the $\psi$ field produces a time-dependent nucleation rate for bubbles of true $\phi$ vacuum. In this model, we find that bubbles of true vacuum can indeed percolate and we argue that thermalization of the interiors can more easily take place. The required degree of flatness (i.e., the fine tuning) in the potential of the $\psi$ field is comparable to that of other models which invoke slowly rolling fields. Pseudo Nambu-Goldstone bosons may naturally provide the flat potential for the rolling field.Comment: 18 pages, 2 figures, This early paper is being placed on the archive to make it more easily accessible in light of recent interest in reviving tunneling inflationary models and as its results are used in an accompanying submissio

Naturally Large Cosmological Neutrino Asymmetries in the MSSM

A large neutrino asymmetry is an interesting possibility for cosmology, which can have significant observable consequences for nucleosynthesis and the cosmic microwave background. However, although it is a possibility, there is no obvious reason to expect the neutrino asymmetry to be observably large. Here we note that if the baryon asymmetry originates via the Affleck-Dine mechanism along a d=4 flat direction of the MSSM scalar potential and if the lepton asymmetry originates via Affleck-Dine leptogenesis along a d=6 direction, corresponding to the lowest dimension directions conserving R-parity, then the ratio n_{L}/n_{B} is naturally in the range 10^{8}-10^{9}. As a result, a potentially observable neutrino asymmetry is correlated with a baryon asymmetry of the order of 10^{-10}.Comment: 10 pages LaTeX. Final version to be published in Physical Review Letter