The 2-Hilbert Space of a Prequantum Bundle Gerbe

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantisation. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantisation in this setting, including its dimensional reduction to ordinary prequantisation.Comment: 97 pages; v2: minor changes; Final version to be published in Reviews in Mathematical Physic

Detailed Phase Transition Study at M_H <= 70 GeV in a 3-dimensional SU(2)SU(2)--Higgs Model

We study the electroweak phase transition in an effective 3-dimensional theory for a Higgs mass of about 70 GeV by Monte Carlo simulations. The transition temperature and jumps of order parameters are obtained and extrapolated to the continuum using multi-histogram techniques and finite size analysis.Comment: Talk presented at LATTICE96(electroweak), 4 pages, 5 figure

Hubbard Model with Luscher fermions - a progress report

Some modifications of the Luscher algorithm, which reduce the autocorelation time, are proposed and tested.Comment: 3 pages, uuencoded gzipped Postscript, contribution to Lattice 9

Physics of the Electroweak Phase Transition at M_H <= 70 GeV in a 3-dimensional SU(2)-Higgs Model

Physical parameters of the electroweak phase transition in a 3d effective lattice SU(2)-Higgs model are presented. The phase transition temperatures, latent heats and continuum condensate discontinuities are measured at Higgs masses of about 70 and 35 GeV. Masses and Higgs condensates are compared to perturbation theory in the broken phase. In the symmetric phase bound states and the static force are determined.Comment: Talk presented at LATTICE96(electroweak), 4 pages, 5 figure

On the scaling of the electroweak interface tension at finite temperature

We determine the interface tension of the finite-temperature electroweak phase transition in a numerical investigation of the SU(2)--Higgs model on a four-dimensional lattice with temporal extension $L_t=3$. In this simulation the chosen parameters correspond to a Higgs boson mass of about 16 GeV. As a result the interface tension shows only small scaling violations in comparison with previous studies for $L_t=2$ lattices. We also report on some experiences with autocorrelations in the applied Monte Carlo simulations of two-phase systems.Comment: 10 pages, latex2e, 7 Postscript figures, uses packages epsfig and amssym

Interface Tension of the Electroweak Phase Transition

In our nonperturbative lattice investigation we study the interface tension of the finite-temperature electroweak phase transition. In this analysis the Higgs mass has been chosen to be about $35$ GeV. At the transition point of a finite volume system, tunnelling between the symmetric and the Higgs phase takes place. This phenomenon leads to a splitting of the ground state, which can be used to determine the interface tension. The result obtained this way agrees with the result of the two-coupling method and with the prediction of the perturbative approach.Comment: 10 pages, five figures in uuencoded PS format, Latex + epsf.st

Numerical Simulations and the Strength of the Electroweak Phase Transition

Numerical simulations are performed to study the finite temperature phase transition in the SU(2) Higgs model on the lattice. The strength of the first order phase transition is investigated by determining the latent heat and the interface tension on $L_t=2$ lattices. The values of the Higgs boson mass presently chosen are below 50 GeV. Our results are in qualitative agreement with two-loop resummed perturbation theory.Comment: (Only a few minor changes compared to the original version.) 9 pages and 2 figures, DESY-94-08

Where does the hot electroweak phase transition end?

We give the nonperturbative phase diagram of the four-dimensional hot electroweak phase transition. A systematic extrapolation $a \to 0$ is done. Our results show that the finite temperature SU(2)-Higgs phase transition is of first order for Higgs-boson masses $m_H<66.5 \pm 1.4$ GeV. The full four-dimensional result agrees completely with that of the dimensional reduction approximation. This fact is of particular importance, because it indicates that the fermionic sector of the Standard Model (SM) can be included perturbatively. We obtain that the Higgs-boson endpoint mass in the SM is $72.4 \pm 1.7$ GeV. Taking into account the LEP Higgs-boson mass lower bound excludes any electroweak phase transition in the SM.Comment: LATTICE98(electroweak), presented by Z. Fodor. Latex, 3 pages, 3 figu res. Comment line change

3-D lattice simulation of the electroweak phase transition at small Higgs mass

We study the electroweak phase transition by lattice simulations of an effective 3-dimensional theory, for a Higgs mass of about $35 GeV$. In the broken symmetry phase our results on masses and the Higgs condensate are consistent with 2-loop perturbative results. However, we find a non-perturbative lowering of the transition temperature, similar to the one previously found at $m_H = 80 GeV$. For the symmetric phase, bound state masses and the static force are determined and compared with results for pure $SU(2)$ theory.Comment: 11 pages, uuencoded ps-file, 5 postscript figures include

Trophic networks improve the performance of microbial anodes treating wastewater

Microbial anodes represent a distinct ecological niche that is characterized mainly by the terminal electron acceptor, i.e., the anode potential, and the substrate, i.e., the electron source. Here, we determine the performance and the biofilm community of anode microbiomes while using substrates of increasing complexity (organic acids or organic acids and sugar or real domestic wastewater) to mimic different, practically relevant, trophic levels. α-Diversity values increased with substrate complexity. In addition, the higher abundance value of Deltaproteobacteria in the biofilms corresponds to higher reactor performance (i.e., COD removal, current density, and Coulombic efficiency). In reactors exploiting real wastewater, the diversity of the planktonic microorganisms was only little affected. Microbiome network analysis revealed two important clusters for reactor performance as well as performance-independent pathogen-containing clusters. Interestingly, Geobacter was not found to be integrated in the network underlining its outstanding individual ecological role in line with its importance for the efficiency of the electron harvest for all reactors. The microbiome analysis of different trophic levels and their temporal development from initial colonization to stable treatment demonstrate important principles for the implementation of microbial anodes for wastewater treatment