(Bosonic)Mass Meets (Extrinsic)Curvature

In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum spontaneously breaks the underlying gauge symmetry if the invariance group of the vacuum is a proper subgroup of the gauge group. We show that each choice of a vacuum admits to geometrically interpret the bosonic mass matrices as ``normal'' sections. The spectrum of these sections turns out to be constant over the manifold and independent of the chosen vacuum. Since the mass matrices commute with the invariance group of the chosen vacuum one may decompose the Hermitian vector bundles which correspond to the bosons in the eigenbundles of the bosonic mass matrices. This decomposition is the geometrical analogue of the physical notion of a ``particle multplet''. In this sense the basic notion of a ``free particle'' also makes sense within the geometrical context of a gauge theory, provided the gauge symmetry is spontaneously broken by some vacuum. We also discuss the Higgs-Kibble mechanism (``Higgs Dinner'') from a geometrical point of view. It turns out that the ``unitary gauge'', usually encountered in the context of discussing the Higgs Dinner, is of purely geometrical origin. In particular, we discuss rotationally symmetric Higgs potentials and give a necessary and sufficient condition for the unitary gauge to exist. As a specific example we discuss in some detail the electroweak sector of the standard model of particle physics in this context.Comment: 26 page

The Future of International Criminal Justice

On March 19, 2008, the Honorable Richard Goldstone, former justice on the Constitutional Court of South Africa, delivered the Georgetown Law Center’s twenty-eithth Annual Philip A. Hart Memorial Lecture: The Future of International Criminal Justice. Goldstone graduated from the University of the Witwatersrand with a BA LLB cum laude in 1962. After graduating, he practiced as an advocate at the Johannesburg Bar. In 1976 he was appointed senior counsel and in 1980 was made a judge of the Transvaal Supreme Court. In 1989 he was appointed to the Appellate Division. From 1991 to 1994 he served as the chairperson of the Commission of Inquiry Regarding Public Violence and Intimidation, which came to be known as the Goldstone Commission. He served as a judge of the Constitutional Court of South Africa from July 1994 to October 2003. From 15 August 1994 to September 1996 he served as the chief prosecutor of the United Nations\u27 International Criminal Tribunals for the former Yugoslavia and Rwanda. From August 1999 until December 2001 he was the chairperson of the International Independent Inquiry on Kosovo. In December 2001 he was appointed the co-chairperson of the International Task Force on Terrorism, which was established by the International Bar Association. In April 2004 the secretary-general of the United Nations appointed Goldstone to the independent committee to investigate the Iraqi oil-for-food program (the Volcker Committee). In October 2007 he was appointed by the Registrars of the United Nations International Criminal Tribunals for the former Yugoslavia and Rwanda to chair an Advisory Committee on the Archiving of the Documents and Records of the two tribunals

Unitization during Category Learning

Five experiments explored the question of whether new perceptual units can be developed if they are diagnostic for a category learning task, and if so, what are the constraints on this unitization process? During category learning, participants were required to attend either a single component or a conjunction of five components in order to correctly categorize an object. In Experiments 1-4, some evidence for unitization was found in that the conjunctive task becomes much easier with practice, and this improvement was not found for the single component task, or for conjunctive tasks where the components cannot be unitized. Influences of component order (Experiment 1), component contiguity (Experiment 2), component proximity (Experiment 3), and number of components (Experiment 4) on practice effects were found. Using a Fourier Transformation method for deconvolving response times (Experiment 5), prolonged practice effects yielded responses that were faster than expected by analytic model that integrate evidence from independently perceived components

Introduction

Given the violence in Darfur and the ensuing international reaction, the Fordham International Law Journal decided to publish a special issue on Darfur. It is timely in light of the continuing violence in the Darfur region. This article serves as the Introduction to the special issue

Introduction

This special issue of the Fordham International Law Journal contains seven outstanding articles by jurists from seven countries on three continents. The articles have a common thread in highlighting the necessity for respect of human rights and the human dignity that they are designed to protect. They also demonstrate the significant advances made since the end of World War II of international human rights law. In an age of terrorism there is an inevitable tension between measures designed to protect the lives of innocent civilians and their fundamental civil liberties

Global U(1) Invariance and Mass Scales in Supersymmetry

In a supersymmetric theory with global U(1) invariance, the spontaneous breaking of the latter without the breaking of supersymmetry is revisited in the case of the most general superpotential of 3 singlet superfields. The interesting possibility of having 2 hierarchical mass scales is pointed out, together with its consequences as applied to the axionic solution of the strong CP problem.Comment: 9 pages, including 1 figur