On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program which are not compatible with the existence of a radiative threshold, predicted by earlier calculations. Second, we carry out a perturbative calculation which helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it accurately reproduces the observed kink dynamics. Fourth, we report on a novel occurrence of length scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.Comment: 19 pages, REVTeX 3.0, 24 figures available from A S o

Quantum Gravitational Bremsstrahlung, Massless versus Massive Gravity

The massive spin-2 quantum gauge theory previously developed is applied to calculate gravitational bremsstrahlung. It is shown that this theory is unique and free from defects. In particular, there is no strong coupling if the graviton mass becomes small. The cross sections go over smoothly into the ones of the massless theory in the limit of vanishing graviton mass. The massless cross sections are calculated for the full tensor theory.Comment: 13 pages, 1 figur

Slowly decaying classical fields, unitarity, and gauge invariance

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the field goes to zero. The importance of this point is exposed for the counter-example of low-dimensionally expanding systems. The issues of gauge invariance and of the interpretation of the evolution at intermediate times are also intricately linked to that point.Comment: 8 pages, no figure

Catalytic Asymmetric Hydroalkoxylation of C–C Multiple Bonds

Asymmetric hydroalkoxylation of alkenes constitutes a redox-neutral and 100% atom-economical strategy toward enantioenriched oxygenated building blocks from readily available starting materials. Despite their great potential, catalytic enantioselective additions of alcohols across a C–C multiple bond are particularly underdeveloped, especially compared to other hydrofunctionalization methods such as hydroamination. However, driven by some recent innovations, e.g., asymmetric MHAT methods, asymmetric photocatalytic methods, and the development of extremely strong chiral Brønsted acids, there has been a gratifying surge of reports in this burgeoning field. The goal of this review is to survey the growing landscape of asymmetric hydroalkoxylation by highlighting exciting new advances, deconstructing mechanistic underpinnings, and drawing insight from related asymmetric hydroacyloxylation and hydration. A deep appreciation of the underlying principles informs an understanding of the various selectivity parameters and activation modes in the realm of asymmetric alkene hydrofunctionalization while simultaneously evoking the outstanding challenges to the field moving forward. Overall, we aim to lay a foundation for cross-fertilization among various catalytic fields and spur further innovation in asymmetric hydroalkoxylations of C–C multiple bonds

The WARPS survey - IV: The X-ray luminosity-temperature relation of high redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity-temperature relation out to high redshift (z~0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fit in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high redshift L-T relation not previously sampled, are compared to existing measurements at low redshift in order to constrain the evolution of the L-T relation. We find a best fit to low redshift (z1 keV, to be L proportional to T^(3.15\pm0.06). Our data are consistent with no evolution in the normalisation of the L-T relation up to z~0.8. Combining our results with ASCA measurements taken from the literature, we find eta=0.19\pm0.38 (for Omega_0=1, with 1 sigma errors) where L_Bol is proportional to (1 + z)^eta T^3.15, or eta=0.60\pm0.38 for Omega_0=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.Comment: 11 pages, 7 figures, accepted for publication in MNRA

Spectral Statistics for the Dirac Operator on Graphs

We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantisation condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation