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

Self-reported pain severity is associated with a history of coronary heart disease

This study was funded by Arthritis Research UK (grant number: 17292).Peer reviewedPublisher PD

q-Symmetries in DNLS-AL chains and exact solutions of quantum dimers

Dynamical symmetries of Hamiltonians quantized models of discrete non-linear Schroedinger chain (DNLS) and of Ablowitz-Ladik chain (AL) are studied. It is shown that for $n$-sites the dynamical algebra of DNLS Hamilton operator is given by the $su(n)$ algebra, while the respective symmetry for the AL case is the quantum algebra su_q(n). The q-deformation of the dynamical symmetry in the AL model is due to the non-canonical oscillator-like structure of the raising and lowering operators at each site. Invariants of motions are found in terms of Casimir central elements of su(n) and su_q(n) algebra generators, for the DNLS and QAL cases respectively. Utilizing the representation theory of the symmetry algebras we specialize to the $n=2$ quantum dimer case and formulate the eigenvalue problem of each dimer as a non-linear (q)-spin model. Analytic investigations of the ensuing three-term non-linear recurrence relations are carried out and the respective orthonormal and complete eigenvector bases are determined. The quantum manifestation of the classical self-trapping in the QDNLS-dimer and its absence in the QAL-dimer, is analysed by studying the asymptotic attraction and repulsion respectively, of the energy levels versus the strength of non-linearity. Our treatment predicts for the QDNLS-dimer, a phase-transition like behaviour in the rate of change of the logarithm of eigenenergy differences, for values of the non-linearity parameter near the classical bifurcation point.Comment: Latex, 19pp, 4 figures. Submitted for publicatio

Determinants of sustained volunteerism in sport organisations in Hong Kong

Oral presentation: abstract 2014-274INTRODUCTION: The crucial role played by volunteers in sport service delivery is well recognised and documented. However, while there has been considerable research on sport volunteers, most studies have been based typically on theories and samples derived from a western context. This study examined determinants of sustained volunteerism in sport organisations in Hong Kong adapting a theoretical model developed by Penner (2002) …postprin

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

Celebrating Stephen Robertson's retirement

Stephen Robertson retired from the Microsoft Research Lab in Cambridge during the summer of 2013 after a long career as one of the most influential, well-liked and eminent researchers in Information Retrieval throughout the world

Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper develops a presentation of these Lie algebras convenient for the context, and derives many properties of the matrices of their defining representations and of the ad-invariant tensors that enter their multiplication laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on fermionic Fock spaces respectively are constructed. Concise general expressions (see (5.2) and (5.5) below) for their L-operators are obtained, and used to derive simple formulas for the T operators of the rational RTT algebra of the associated integral systems, thereby enabling their efficient treatment by means of the algebraic Bethe ansatz.Comment: 24 pages, LaTe

High-Resolution Chandra Spectroscopy Of Tau Scorpii: A Narrow-Line X-Ray Spectrum From A Hot Star

Long known to be an unusual early-type star by virtue of its hard and strong X-ray emission, tau Scorpii poses a severe challenge to the standard picture of O-star wind-shock X-ray emission. The Chandra HETGS spectrum now provides significant direct evidence that this B0.2 star does not fit this standard wind-shock framework. The many emission lines detected with the Chandra gratings are significantly narrower than what would be expected from a star with the known wind properties of tau Sco, although they are broader than the corresponding lines seen in late-type coronal sources. While line ratios are consistent with the hot plasma on this star being within a few stellar radii of the photosphere, from at least one He-like complex there is evidence that the X-ray emitting plasma is located more than a stellar radius above the photosphere. The Chandra spectrum of Sco is harder and more variable than those of other hot stars, with the exception of the young magnetized O star theta(1) Ori C. We discuss these new results in the context of wind, coronal, and hybrid wind-magnetic models of hot-star X-ray emission

The open future, bivalence and assertion

It is highly intuitive that the future is open and the past is closed—whereas it is unsettled whether there will be a fourth world war, it is settled that there was a first. Recently, it has become increasingly popular to claim that the intuitive openness of the future implies that contingent statements about the future, such as ‘there will be a sea battle tomorrow,’ are non-bivalent (neither true nor false). In this paper, we argue that the non-bivalence of future contingents is at odds with our pre-theoretic intuitions about the openness of the future. These are revealed by our pragmatic judgments concerning the correctness and incorrectness of assertions of future contingents. We argue that the pragmatic data together with a plausible account of assertion shows that in many cases we take future contingents to be true (or to be false), though we take the future to be open in relevant respects. It follows that appeals to intuition to support the non-bivalence of future contingents is untenable. Intuition favours bivalence