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

The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly

We complete our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac Fermions. We consider the consistency of the model up to the third order of the perturbation theory. In the second order we obtain pure group theoretical relations expressing a representation property of the numerical coefficients appearing in the left and right handed components of the interaction Lagrangian. In the third order of the perturbation theory we obtain the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate

CP Asymmetry in Charged Higgs Decays in MSSM

We discuss and compare the charge-parity (CP) asymmetry in the charged Higgs boson decays H -> \bar{u}_i d_j for the second and third generation quarks in the minimal supersymmetric standard model. As part of the analysis, we derive some general analytical formulas for the imaginary parts of two-point and three-point scalar one-loop integrals and use them for calculating vectorial and tensorial type integrals needed for the problem under consideration. We find that, even though each decay mode has a potential to yield a CP asymmetry larger than 10%, further analysis based on the number of required charged Higgs events at colliders favors the \bar{t}b, \bar{c}b, and \bar{c}s channels, whose asymmetry could reach 10-15% in certain parts of the parameter space.Comment: 25 pages, 9 figures. Discussion about charged Higgs observability added, typos corrected, accepted for publication in PR

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

Equilibrium distributions in thermodynamical traffic gas

We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution (for a=1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in microscopical structure of traffic sample depending on traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.Comment: 5 pages, 6 figures, changed content, added reference

The Interaction of Quantum Gravity with Matter

The interaction of (linearized) gravitation with matter is studied in the causal approach up to the second order of perturbation theory. We consider the generic case and prove that gravitation is universal in the sense that the existence of the interaction with gravitation does not put new constraints on the Lagrangian for lower spin fields. We use the formalism of quantum off-shell fields which makes our computation more straightforward and simpler.Comment: 25 page

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

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

Quantum cat maps with spin 1/2

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices. In particular, we show that the diagonal approximation of the spectral form factor for small arguments agrees with the CSE prediction. The results are confirmed by numerical investigations.Comment: 26 pages, 3 figure