On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT

We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega = v_0 k + a + b/k + ..., where the limiting velocity v_0 is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m_q. We compute a and b in terms of the meson quantum numbers and T/m_q. The limiting meson velocity v_0 becomes much smaller than the speed of light at temperatures below but close to T_diss, the temperature above which no meson bound states at rest in the plasma are found. From our result for v_0, we find that the temperature above which no meson bound states with velocity v exist is T_diss(v) \simeq (1-v^2)^(1/4) T_diss, up to few percent corrections.We thus confirm by direct calculation of meson dispersion relations a result inferred indirectly in previous work via analysis of the screening length between a static quark and antiquark in a moving plasma. Although we do not do our calculations in QCD, we argue that the qualitative features of the dispersion relation we compute, including in particular the relation between dissociation temperature and meson velocity, may apply to bottomonium and charmonium mesons propagating in the strongly coupled plasma of QCD. We discuss how our results can contribute to understanding quarkonium physics in heavy ion collisions.Comment: 57 pages, 12 figures; references adde

Stacking sequences for extensionally isotropic, fully isotropic and quasi-homogeneous orthotropic laminates

Stacking sequence listings are presented for fully uncoupled Extensionally Isotropic (EILs), Fully Isotropic (FILs) and Quasi-Homogeneous Orthotropic (QHOLs) angle-ply Laminates, with up to 21 plies. All are sub-sets of a definitive list of Fully Orthotropic Laminates (FOLs), containing generally non-symmetric stacking sequences that are characterized in terms of angle- and cross-ply sub-sequence symmetries. Dimensionless parameters are given for each stacking sequence, from which the ABD matrix is readily derived. Expressions relating these dimensionless parameters to the well-known lamination parameters are also given, together with graphical representations of the feasible domains for Pi/3 and Pi/4 EILs and angle-ply QHOLs containing two and three ply orientations. The feasible domain for Pi/3 FILs is represented graphically by a single point, whereas the domain for angle-ply QHOLs containing four ply orientations is represented by a single stacking sequence

Octopus follow-up: 20 year prognosis in patients randomized to on-pump CABG, off-pump CABG or PCI

BACKGROUND: The very long-term outcomes of off-pump versus on-pump Coronary Artery Bypass Grafting (CABG) and Percutaneous Coronary Intervention (PCI) are largely unclear. We linked 20-years outcomes of two randomized trials to evaluate re-intervention and mortality outcomes for on-pump CABG, off-pump CABG and PCI. METHODS: A data linkage project was performed using data as registered within the Netherlands Heart Registration (NHR), Statistics Netherlands (CBS) and the Octopus trials. Between 1998 and 2000, these trials randomized patients with coronary artery disease to on-pump versus off-pump CABG (OctoPump trial), or to PCI versus off-pump CABG (OctoStent trial). With data linkage, the original 5 years follow-up time for clinical events was extended to 20 years, including mortality and coronary reinterventions. RESULTS: After 20 years, in the OctoPump trial all-cause mortality was 50.0% after on-pump, and 46.5% after off-pump CABG. There was no difference in the combined outcome of mortality and re-interventions (HR 0.82, 95% CI 0.59-1.12). In the OctoStent trial, all-cause mortality was 56.7% after PCI and 52.5% after off-pump CABG. There was no difference in the combined outcome of mortality and re-interventions (HR 0.76, 95% CI 0.57-1.04). Off-pump CABG patients underwent less re-interventions than PCI patients (HR 0.52, 95% CI 0.33-0.80). CONCLUSION: This study revealed no differences in 20-year survival between patients randomized to on-pump versus off-pump CABG, or to PCI versus off-pump-CABG. However, off-pump CABG patients underwent less re-interventions than PCI patients

The Global Financial Crisis: Decoupling of East Asia – Myth or Reality?

The decoupling of East Asia from its economic interactions - both in trade and finance - with the rest of the world refers to the phenomenon of a weakening of the impact of demand and supply shocks emanating from the advanced countries on the region's economic performance since the early 1990s. Available empirical evidence, including the faster recovery of East Asia from the 2008 global economic crisis, does not appear to lend credence to the decoupling thesis. However, with increases in income throughout the region and the three free trade agreements (FTAs) of the People's Republic of China (PRC), Japan, and Korea with the Association of Southeast Asian Nations (ASEAN) (which have entered into force), East Asia will witness a continuing expansion in intra-regional trade, much of which will consist of horizontal intra-industry trade. At the same time, if East Asia succeeds in instituting an efficient capital control regime and in strengthening the Chiang Mai Initiative Multilateralization (CMIM), it will be able to cope better with the volatility of capital flows to the region. Together these developments will then help speed up economic integration among ASEAN+3 member states to build a region that is more self-contained than it has been