Differential calculus on the quantum Heisenberg group

The differential calculus on the quantum Heisenberg group is conlinebreak structed. The duality between quantum Heisenberg group and algebra is proved.Comment: AMSTeX, Pages

Eliashberg's proof of Cerf's theorem

Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method.Comment: 32 page

Can restenosis after coronary angioplasty be predicted from clinical variables?

AbstractObjectives. The purpose of this study was to determine whether variables shown to correlate with restenosis in one group (learning group) could be shown to predict recurrent stenosis in a second group (validation group).Background. Restenosis remains a critical limitation after percutaneous transluminal coronary angioplasty. Although several clinical variables have been shown to correlate with restenosis, there are few data concerning attempts to predict recurrent stenosis.Methods. The source of data was the clinical data bese at Emory University. Patients who had had previous coronary surgery and patients who underwent coronary angioplasty in the setting of acute myocardial Infarction were excluded. A total of 4,006 patients with angiographic restudy after successful angioplisty were identified. They were classified into a learning group of 2,500 patients and a validation group of 1,506 patients. The correlates of restenosis in the learning group were determined by stepwise logistic regression, and a model was developed to predict the probability of restenosis and was tested in the validation group. By using various cut points for the predicted probability of restenosis, a receiver operating characteristic curve was created. Goodness of fit of the model was evaluated by comparing average predicted probabilities with average observed probabilities within subgroups on the basis of risk level determined by linear regression analysis.Results. In the learning group 1,145 patients had restenosis and 1,355 did not. Correlates of restenosis were severe angina, severe diameter stenosis before angioplasty, left anterior descending coronary artery dilation, diabetes, greater diameter stenosis after angioplasty, hypertension, absence of an intimal tear, eccentric morphology and older patient age. The model derived from the learing group was used to predict restenosis in the validation group. By varying the cut point for the predicted probability of restenosis above which restenosis is diagnosed and below which it is not, a receiver operating characteristic curve was created. The curve was close to the line of identity, reflecting a poor predictive ability. However, the model was shown to fit well with the predicted probability of restenosis correlating well with the observed probability (r = 0.98, p = 0.0001).Conclusions. Clinical variables provide limited ability to predict definitively whether a particular patient will have restenosis. However, the current model may be used to predict the probability of restenosis, with some uncertainty, at least in well characterized patients who have already had angioplasy

Scalar field theory on κ\kappa-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J. Mod. Phys.

Dynamical origin of the ⋆θ\star_\theta-noncommutativity in field theory from quantum mechanics

We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory.Comment: 17 pages, to be published in Phys. Lett.

κ\kappa-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure

The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare superalgebra can be written as graded bicrossproduct. We show that the $\kappa$-deformed $D=4$ superalgebra acts covariantly on $\kappa$-deformed chiral superspace.Comment: 13 pages, late

Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F^3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F^2 and F^3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F^2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter.Comment: 36 pages, 25 figures, Latex fil