Lsdiff M and the Einstein Equations

We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a constant connection on flat spacetime.Comment: 5 pages, no figures, Latex, uses amsfonts, amssym.def and amssym.tex. Note added on more direct connection with Yang-Mills equation

The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-instanton moduli space. This action simply corresponds to a scaling of the moduli space.Comment: AMSLatex, 19 pages, no figures. Some discussions clarified, and citations made more accurate. I am grateful to the referee for detailed comments. Version to appear in Communications in Mathematical Physic

A Spinorial Hamiltonian Approach to Gravity

We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variables. In higher dimensions, the theory can either be reduced to a spinorial version of the ADM formalism, or can be left in a more general form which seems useful for the investigation of some spinorial problems such as Riemannian manifolds with reduced holonomy group. In dimensions $0 \pmod 4$, the theory may be recast solely in terms of structures on the positive spin-bundle $\mathbb{V}^+$, but such a reduction does not seem possible in dimensions $2 \pmod 4$, due to algebraic properties of spinors in these dimensions.Comment: 20 pages, Latex 2e. Published versio

Cosmic Strings and Chronology Protection

A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analysed and is found that, away from the strings, the space is identical to a generalised Misner space. The vacuum expectation value of the energy momentum tensor for a conformally coupled scalar field is calculated on this generalised Misner space. It is found to diverge very weakly on the Chronology horizon, but more strongly on the polarised hypersurfaces. The divergence on the polarised hypersurfaces is strong enough that when the proper geodesic interval around any polarised hypersurface is of order the Planck length squared, the perturbation to the metric caused by the backreaction will be of order one. Thus we expect the structure of the space will be radically altered by the backreaction before quantum gravitational effects become important. This suggests that Hawking's `Chronology Protection Conjecture' holds for spaces with non-compactly generated Chronology horizon.Comment: 15 pages, plain TeX, 2 figures (not included), DAMTP-R92/3

The WTO and the Cartagena Protocol: International Policy Coordination or Conflict?

International policy coordination is a challenging exercise requiring policy rapprochement among sovereign nations that often have very different political economy situations. Successful efforts may even result in the creation of multilateral paradigms such as trade agreements or multilateral environmental agreements (MEAs). Typically, there is overlap between these independent paradigms; sometimes in the nexus there is policy coordination and other times there is conflict. An understanding of the factors that account for coordination and conflict is crucial in ensuring that any benefits from policy coordination that may be achieved in one paradigm are not eroded through conflicts with another paradigm. This article presents a case study of the implications of overlapping multilateral paradigms – the World Trade Organization and an MEA known as the Cartagena Protocol on Biosafety – for international market access of biotechnology-based agri-food products.Agricultural and Food Policy, International Relations/Trade,

Increasing the Openness of the Trade Policy Process: Challenges and Implications

Trade policy – once a subset of foreign policy far removed from domestic concern, focused squarely on border issues and subject to the rules of international diplomacy – is now a central concern on the public policy agenda as trade issues have become increasingly entwined with traditionally domestic policy issues. Consequently, demands have been made for more openness in trade policy formation and, in response, many governments have undertaken openness initiatives. Despite these developments there has been only a little research into the increased openness of trade policy processes in general and no research aimed at developing a consistent framework for categorizing various openness initiatives and permitting a meaningful comparison of initiatives between trading partners. In this paper, the general issue of increasing the openness of trade policy is examined, an openness framework is proposed and the implications for trade policy are assessed.openness, openness framework, trade policy, transparency, International Relations/Trade,