Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations

This paper deals with the striking fact that there is an essentially canonical path from the $i$-th Lie algebra cohomology cocycle, $i=1,2,... l$, of a simple compact Lie algebra \g of rank $l$ to the definition of its primitive Casimir operators $C^{(i)}$ of order $m_i$. Thus one obtains a complete set of Racah-Casimir operators $C^{(i)}$ for each \g and nothing else. The paper then goes on to develop a general formula for the eigenvalue $c^{(i)}$ of each $C^{(i)}$ valid for any representation of \g, and thereby to relate $c^{(i)}$ to a suitably defined generalised Dynkin index. The form of the formula for $c^{(i)}$ for $su(n)$ is known sufficiently explicitly to make clear some interesting and important features. For the purposes of illustration, detailed results are displayed for some classes of representation of $su(n)$, including all the fundamental ones and the adjoint representation.Comment: Latex, 16 page

Hidden supersymmetries in supersymmetric quantum mechanics

We discuss the appearance of additional, hidden supersymmetries for simple 0+1 $Ad(G)$-invariant supersymmetric models and analyse some geometrical mechanisms that lead to them. It is shown that their existence depends crucially on the availability of odd order invariant skewsymmetric tensors on the (generic) compact Lie algebra $\cal G$, and hence on the cohomology properties of the Lie algebra considered.Comment: Misprints corrected, two refs. added. To appear in NP

Modelling rheumatoid arthritis : a hybrid modelling framework to describe pannus formation in a small joint

Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of these aspects, to date there are few such models that can be used to better understand the disease. As a first step in the mechanistic understanding of RA, in this study we introduce a new hybrid mathematical modelling framework that describes pannus formation in a small proximal interphalangeal (PIP) joint. We perform numerical simulations with this new model, to investigate the impact of different levels of immune cells (macrophages and fibroblasts) on the degradation of bone and cartilage. Since many model parameters are unknown and cannot be estimated due to a lack of experiments, we also perform a sensitivity analysis of model outputs to various model parameters (single parameters or combinations of parameters). Finally, we discuss how our model could be applied to investigate current treatments for RA, for example, methotrexate, TNF-inhibitors or tocilizumab, which can impact different model parameters.Publisher PDFPeer reviewe

Invariant tensors for simple groups

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.Comment: Latex file. 34 pages. (Trivial) misprints corrected. To appear in Nucl. Phys.

Hyperkahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace

Kahler manifolds have a natural hyperkahler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N = 2 models on the tangent bundles of some classical Hermitian symmetric spaces (specifically, the four regular series of irreducible compact symmetric Kahler manifolds, and their non-compact versions). A further dualization yields the Kahler potential for the hyperkahler metric on the cotangent bundle.Comment: 47 pages, typos corrected, version accepted by JHE

Evaluation of work-related psychosocial factors and regional musculoskeletal pain: results from a EULAR Task Force

Objectives: to establish whether review articles provide consistent conclusions on associations between workplace psychosocial factors and musculoskeletal pain and, if differences exist, to explore whether this is related to the methods used.Methods: reviews, reported up to February 2007, that included consideration of workplace psychosocial factors and upper limb, back or knee pain were identified through searches of multiple databases. The specific work-related psychosocial factors considered were job demands, support, job autonomy and job satisfaction. The conclusions of each review on one or more of the psychosocial/musculoskeletal pain associations were extracted.Results: 15 review articles were identified that considered one or more of the regional pain syndromes included in the study. For back pain, the most consistent conclusions (four reviews positive out of six) were with high job demands and low job satisfaction. The studies of upper limb pain were exclusively related to shoulder and/or neck pain, and the most consistent positive conclusions were with high and low job demands (four reviews positive out of six and two reviews positive out of three, respectively). For knee pain, only a single review was identified. For individual reviews of back and upper limb pain, there were marked differences in the number of associations concluded to be positive between reviews.Conclusions: the reasons for reviews coming to different conclusions included that they were often evaluating different bodies of evidence (according to their search criteria, the year when the review was conducted, the role that quality assessment played in whether studies contributed to evidence, and the combination of risk factors addressed in individual studies), but more important was whether the review specified explicit criteria for making conclusions on strength of evidence. These conclusions emphasise the importance of developing standardised methods for conducting such evaluations of existing evidence and the importance of new longitudinal studies for clarifying the temporal relationship between psychosocial factors and musculoskeletal pain in the workplac

Classical integrable lattice models through quantum group related formalism

We translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical integrable models. Thus new as well as known lattice systems of different classes are generated including new types of collective integrable models and canonical models with nonstandard $r$ matrices.Comment: 7 pages; Talk presented at NEEDS'93 (Gallipoli,Italy

Generalized quantum field theory: perturbative computation and perspectives

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we construct a quantum field theory that creates at any space-time point particles described by a q-deformed Heisenberg algebra and we compute the propagator and a specific first order scattering process. Concerning the second one, we draw attention to the possibility of constructing this theory where each state of a generalized Heisenberg algebra is interpreted as a particle with different mass.Comment: 19 page

Supersymmetry from a braided point of view

We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and covariant derivative are obtained in the limit in question as the left and right derivatives of the calculus on the braided line.Comment: LateX file. 10 pages. To appear in Phys. Lett.