Lie algebra and invariant tensor technology for g2

Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representation gamma and the full set of invariant tensors that arise in relation thereto. A comprehensive listing of identities involving these tensors is given. This includes identities that depend on use of characteristic equations, especially for gamma, and a good body of results involving the quadratic, sextic and (the non-primitivity of) other Casimir operators of g2.Comment: 29 pages, LaTe

On characteristic equations, trace identities and Casimir operators of simple Lie algebras

Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for `small' Lie algebras and suitable for treatment by computer algebra. A very large body of new results emerges in the forms, a) of identities of a tensorial nature, involving structure constants etc. of g, b) of trace identities for powers of matrices of the adjoint and defining representations of g, c) of expressions of non-primitive Casimir operators of g in terms of primitive ones. The methods are sufficiently tractable to allow not only explicit proof by hand of the non-primitive nature of the quartic Casimir of g2, f4, e6, but also e.g. of that of the tenth order Casimir of f4.Comment: 39 pages, 8 tables, late

Quantum Technology: The Second Quantum Revolution

We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including; quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.Comment: 24 pages and 6 figure

Blood rheology, cardiovascular risk factors, and cardiovascular disease: The West of Scotland Coronary Prevention Study

The West of Scotland Coronary Prevention Study (WOSCOPS) showed that pravastatin reduced the risk of coronary heart disease (CHD) events in 6,595 middle-aged hypercholesterolaemic men aged 45-64 years without prior myocardial infarction followed for an average of 4.9 years. We hypothesised prospectively (a) that baseline levels of haemorheological variables were related to baseline and incident CHD and to mortality; and (b) that reduction in lipoproteins by pravastatin would lower plasma and blood viscosity, a potential contributory mechanism to CHD events. We therefore studied plasma and blood viscosity, fibrinogen, haematocrit, and blood cell counts at baseline and 1 year. At baseline, plasma and blood viscosity were related to risk factors, CHD measures, and claudication. On univariate analysis, baseline levels of all rheological variables (except platelet count) were related to incident CHD; CHD mortality; and total mortality. On multivariate analysis including baseline CHD and risk factors, plasma and blood viscosity, haematocrit and white cell count each remained significantly associated with incident CHD; while fibrinogen remained an independent predictor of mortality (all p<0.03). After one year, lipoprotein reduction by pravastatin was associated with significant reductions (about one quarter of a standard deviation) in plasma viscosity (mean difference 0.02 mPa.s, p<0.001) and in blood viscosity (mean difference 0.06 mPa.s, p<0.001), but was not associated with significant changes in other rheological variables. We therefore suggest that pravastatin therapy, which reduces elevated lipoproteins in hypercholesterolaemic men, may lower risks of CHD and mortality partly by lowering plasma and blood viscosity. Further studies are required to test this hypothesis

Real Forms of the Oscillator Quantum Algebra and its Representations

We consider the conditions under which the $q$-oscillator algebra becomes a Hopf $*$-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown that they are related to ${\text {su}}_{q^{1/2}}(2)$ with different conjugations.Comment: 10 pages, Ams-Tex, To be published in Letters in Mathematical physic

On Macroscopic Energy Gap for qq-Quantum Mechanical Systems

The q-deformed harmonic oscillator within the framework of the recently introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that for "physical" values $q\sim1$, the gap between the energy levels decreases with growing energy. Comparing with the other (real) $q$-deformations of the harmonic oscillator, where the gap instead increases, indicates that the formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum Mechanics may be avoided.Comment: 6 pages, TeX, PRA-HEP-92/1