Natural star products on symplectic manifolds and quantum moment maps

We define a natural class of star products: those which are given by a series of bidifferential operators which at order $k$ in the deformation parameter have at most $k$ derivatives in each argument. We show that any such star product on a symplectic manifold defines a unique symplectic connection. We parametrise such star products, study their invariance and give necessary and sufficient conditions for them to yield a quantum moment map. We show that Kravchenko's sufficient condition for a moment map for a Fedosov star product is also necessary.Comment: Expanded bibliograph

Understanding the UK's soft power: more than Shakespeare and the Royal Family

Do we understand enough about what soft power is? Gary Rawnsley explains that although the focus has so far been on cultural icons and stories, there is another important aspect to soft power: the actions of the British government. These are seen as a reflection of the values the UK upholds, and so influence opinions overseas. He argues that understanding this dimension of soft power is becoming more urgent as Brexit approaches

Twistor theory of symplectic manifolds

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then, after recalling the construction of the almost complex structure induced on $Z$ by a symplectic connection on M, we study and find some specific properties of both. We show a few examples of twistor spaces, develop the interplay with the symplectomorphisms of M, find some results about a natural almost Hermitian structure on $Z$ and finally prove its n+1-holomorphic completeness. We end by proving a vanishing theorem about the Penrose transform.Comment: 34 page

Monopole-charge instability

For monopoles with nonvanishing Higgs potential it is shown that with respect to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to that of a pure gauge theory on the two-sphere (b) each topological sector admits one, and only one, stable monopole charge, and (c) each unstable monopole admits $2\sum_{q<0} (2|q|-1)$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres. The general theory is illustrated for the little groups U(2), U(3), SU(3)/Z_3 and O(5).Comment: LaTex, 38 pages. 7 figures and 2 photos. Posted for the record. Originally published 20 years ago, with Note added in 2009: Hommage to Lochlainn O'Raifeartaigh and Sidney Coleman. Some typos correcte

To Know Us is to Love Us:Public Diplomacy and International broadcasting in Contemporary Russia and China

China and Russia have devoted significant resources to developing their international broadcasting capacity as an instrument of public diplomacy. Focusing on CCTV-N (China) and RT (Russia), this article discusses the strategies each has developed to communicate with international audiences and further the foreign policy ambitions of policy makers in Beijing and Moscow. It highlights the differences between the two stations - namely CCTV-N's ambition to rectify perceived distortions in the global flow of news about China, and RT's focus on reporting events in the US. Hence the case studies expose the fine line between propaganda and public diplomacy. © 2015 Political Studies Association and John Wiley & Sons Ltd

Introduction to “International Broadcasting and Public Diplomacy in the 21st Century”

International broadcasting remains a key activity in public diplomacy. In this Introduction I discuss how international broadcasting has long been associated with the projection of foreign policy interests, from an instrument of empire building in the 1920s and 1930s, through the Cold War and beyond. In particular, the Introduction evaluates how modern Information Communications Technologies, especially the internet and social media, have transformed the way international broadcasting contributes to public diplomacy