Analytic Cohomology on Blown - Up Twistor Space

A flat twistor space is a complex 3 - manifold having the property that every point of the manifold has a neighbourhood which is biholomorphic to a neighbourhood of a complex projective line in complex projective 3 - space. The Penrose transform provides an isomorphism between holomorphic structures on twistor spaces and certain field equations on (Riemannian or Lorentzian) space - times. The initial examples studied by Penrose were solutions to zero rest mass equations and, amongst these, the elementary states were of particular interest. These were elements of a sheaf cohomology group having a singularity on a particular complex projective line, with a codimension-2 structure similar, in some sense, to a Laurent series with a pole of finite order. In this work we extend this idea to the notion of codimension-2 poles for analytic cohomology classes on a punctured flat twistor space, by which we mean a general, compact, flat, twistor space with a finite number of non-intersecting complex, projective lines removed. We define a holomorphic line bundle on the blow-up of the compact flat twistor space along these lines and show that elements of the first cohomology group with coefficients in the line bundle, when restricted to the punctured twistor space, are cohomology classes with singularities on the removed lines which have precisely the kind of codimension - 2 structure which we define as codimension-2 poles. The dimension of this cohomology group on the blown-up manifold is then calculated for the twistor space of a compact, Riemannian, hyperbolic 4-manifold. The calculation uses the Hirzebruch - Riemann - Roch theorem to find the holomorphic Euler characteristic of the line bundle, (in chapter 3) together with vanishing theorems. In chapter 4 we show that it is sufficient to find vanishing theorems for the compact flat - twistor space. In chapter 5 we prove a number of vanishing theorems to be used. The technique uses the Penrose transform to convert the theorem to a vanishing theorem for spinor fields. These are then proved by using Penrose's Spinor calculus

Charged Particles: A Builder's Guide

It is sometimes claimed that one cannot describe charged particles in gauge theories. We identify the root of the problem and present an explicit construction of charged particles. This is shown to have good perturbative properties and, asymptotically before and after scattering, to recover particle modes.Comment: 6 pages, LaTeX, to appear in proceedings of Sixth Workshop on Non-Perturbative Quantum Chromodynamics, Paris, June 200

Asymptotic Dynamics in Quantum Field Theory

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.Comment: 18 pages, 3 figure

Architecture and Agency For Equity In Areas Beyond National Jurisdiction

The United Nations (UN) Sustainable Development Goals (SDGs) and the UN Decade of Ocean Science for Sustainable Development (Ocean Decade) bring increased attention to various aspects of ocean governance, including equity. One of the Ocean Decade\u27s identified challenges is to develop a sustainable and equitable ocean economy, but questions arise about how to conceptualize the multiple dimensions of equity in an ocean context. These questions become more complex as activities move away from coastal ecosystems and communities into off-shore Areas Beyond National Jurisdiction (ABNJ), where ocean resources are recognized simultaneously as unowned/open access and as common heritage. In this paper, we mobilize the Earth System Governance analytics of ‘architecture’ and ‘agency’, to reflect on the possibilities for equity in ABNJ. Motivated by the general attention to equity in UN initiatives like the SDGs and the Ocean Decade, we describe current UN architecture for ocean governance, including principles that might support equity. Existing UN architecture focuses on distributional equity among nation states, with less attention to recognitional or procedural equity. State actors have most agency, while non-state actors can exercise some via broad UN declarations and through mechanisms like ‘major groups.’ We use on-going negotiations in the International Seabed Authority on rules for mineral exploitation and in the Intergovernmental Conference on an international legally binding instrument under UNCLOS on the conservation and sustainable use of marine biological diversity of Areas Beyond National Jurisdiction to illustrate how existing architecture shapes possibilities for equity in ABNJ. As new governance possibilities are imagined, attending to existing architecture and agency can help avoid further entrenching existing power imbalances and unwittingly reproducing or exacerbating inequities

Charges in Gauge Theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the Abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green's functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.Comment: 47 pages, LaTeX, 14 figures, uses feynmp, necessary Metapost files included. Review to appear in Pramana, Journal of Physics. Minor LaTeX change to make page numbers visible on "Letter" paper forma

Basic science232. Certolizumab pegol prevents pro-inflammatory alterations in endothelial cell function

Background: Cardiovascular disease is a major comorbidity of rheumatoid arthritis (RA) and a leading cause of death. Chronic systemic inflammation involving tumour necrosis factor alpha (TNF) could contribute to endothelial activation and atherogenesis. A number of anti-TNF therapies are in current use for the treatment of RA, including certolizumab pegol (CZP), (Cimzia ®; UCB, Belgium). Anti-TNF therapy has been associated with reduced clinical cardiovascular disease risk and ameliorated vascular function in RA patients. However, the specific effects of TNF inhibitors on endothelial cell function are largely unknown. Our aim was to investigate the mechanisms underpinning CZP effects on TNF-activated human endothelial cells. Methods: Human aortic endothelial cells (HAoECs) were cultured in vitro and exposed to a) TNF alone, b) TNF plus CZP, or c) neither agent. Microarray analysis was used to examine the transcriptional profile of cells treated for 6 hrs and quantitative polymerase chain reaction (qPCR) analysed gene expression at 1, 3, 6 and 24 hrs. NF-κB localization and IκB degradation were investigated using immunocytochemistry, high content analysis and western blotting. Flow cytometry was conducted to detect microparticle release from HAoECs. Results: Transcriptional profiling revealed that while TNF alone had strong effects on endothelial gene expression, TNF and CZP in combination produced a global gene expression pattern similar to untreated control. The two most highly up-regulated genes in response to TNF treatment were adhesion molecules E-selectin and VCAM-1 (q 0.2 compared to control; p > 0.05 compared to TNF alone). The NF-κB pathway was confirmed as a downstream target of TNF-induced HAoEC activation, via nuclear translocation of NF-κB and degradation of IκB, effects which were abolished by treatment with CZP. In addition, flow cytometry detected an increased production of endothelial microparticles in TNF-activated HAoECs, which was prevented by treatment with CZP. Conclusions: We have found at a cellular level that a clinically available TNF inhibitor, CZP reduces the expression of adhesion molecule expression, and prevents TNF-induced activation of the NF-κB pathway. Furthermore, CZP prevents the production of microparticles by activated endothelial cells. This could be central to the prevention of inflammatory environments underlying these conditions and measurement of microparticles has potential as a novel prognostic marker for future cardiovascular events in this patient group. Disclosure statement: Y.A. received a research grant from UCB. I.B. received a research grant from UCB. S.H. received a research grant from UCB. All other authors have declared no conflicts of interes