6,847 research outputs found
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 (-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
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