Review of the Phenomenology of Noncommutative Geometry

We present a pedagogical review of particle physics models that are based on the noncommutativity of space-time, $[\hat{x}_\mu,\hat{x}_\nu]=i \theta_{\mu \nu}$, with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur for example in a future $e^+e^-$ linear collider with $\sqrt{s} = 500 GeV$, as well as low energy experiments such as those pertaining to elementary electric dipole moments and other \cpviolng observables, and finally comment on the status of phenomenological work in cosmology and extra dimensions.Comment: updated, references added, corrected typo

Linear systems with adiabatic fluctuations

We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of fluctuations and 1/|\mu| refers to the time scale of evolution of the unperturbed system to obtain a linear differential equation for the average solution. The theory is applied to the problems of a damped harmonic oscillator and diffusion in a turbulent fluid. The result is the realization of `renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page

Present and Future Aspects of CP Violation

This series of five lectures describes aspects of CP violation, emphasizing its description within the standard electroweak model. After discussing the kaon system, the only place in which CP violation has been seen so far, we turn to the leading contender for the effect, complex phases in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. A number of suggestions are made for improved tests of the standard picture. Hadrons containing $b$ quarks play a key role in this program, and are discussed separately. We also mention a number of non-standard and speculative aspects of CP violation, including alternatives to the CKM description, direct tests of time reversal invariance, and baryogenesis.Comment: 58 pages, latex, 14 uuencoded figures sent separatel

Predictive Control of Linear Uncertain Systems

Predictive control is a very useful tool in controlling constrained systems, since the constraints can be satisfied explicitly by the optimisations. Sets, namely, reachable sets, controllable sets, invariant sets, etc, play fundamental roles in designing predictive control strategies for uncertain systems. Meanwhile, in addition to the commonly assumed boundedness of the uncertainty, the explicit use of its stochastic properties can lead to imprq\fement in system response. This thesis is concerned with robust set theories, mainly for reachable sets, with applications to time-optimal control; and the use of stochastic properties of the uncertainty to achieve less conservative controls. In the first part of this thesis, we focus on LTI systems subject to, additional to the usual constraints, a constraint on the control change between sample times. One key ingredient in controlling such constrained systems is the initial control value, which, via analyses and simulations, is shown to be a useful extra degree of freedom. Reachable sets that incorporate this influential initial control value are derived and analyzed, with theoretical as well as computational algorithms developed for both nominal and uncertain systems under different types of feedback policy. Following this, the reachable set is discussed in connection with time-optimal control to obtain desired control laws. In addition, controllable sets, stabilisable sets and invariant sets for such constrained uncertain systems are studied. In the second part, the uncertainties are assumed to have stochastic properties. They are exploited in three different ways: the expected worst-case is used instead of the worst-case to achieve less conservative control even when the uncertainty is relatively large; the stochastic invariant set is proposed to provide alternative methods for approximating disturbance invariant sets; the relaxed set difference is developed to obtain less restrictive controls and/or replacing probabilistic constraint or slack variables.Imperial Users onl

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free -- a feature characteristic of Dirac's `` point-form\rq\rq of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincar\'e generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.Comment: 30 page

Hierarchical Four-Neutrino Oscillations With a Decay Option

We present a new and novel synthesis of all existing neutrino data regarding the disappearance and appearance of $\nu_e$ and $\nu_\mu$. We assume four neutrinos: $\nu_e, \nu_\mu, \nu_\tau$, as well as a heavier singlet neutrino $\nu_s$ of a few eV. The latter may decay into a massless Goldstone boson (the singlet Majoron) and a linear combination of the doublet antineutrinos. We comment on how this scenario may be verified or falsified in future experiments.Comment: 13 pages, no figur

Top quark production near threshold

The present theoretical status of top quark pair production near threshold at (future) $e^+ e^-$ ($\mu^+\mu^-$) colliders is summarized.Comment: 8 pages, LaTeX, Talk presented at the High Energy Physics International Euroconference on Quantum Chromodynamics (QCD'99), Montpellier, France, 7-13 July 199