We construct a toric generalised K\"ahler structure on \(\mathbb{C}P^2\) and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic ...functions. We also compute the generalised K\"ahler potential in terms of integrals of elliptic functions.
We study a class of Poisson-Nijenhuis systems defined on compact hermitian symmetric spaces, where the Nijenhuis tensor is defined as the composition of Kirillov-Konstant-Souriau symplectic form with ...the so called Bruhat-Poisson structure. We determine its spectrum. In the case of Grassmannians the eigenvalues are the Gelfand-Tsetlin variables. We introduce the abelian algebra of collective hamiltonians defined by a chain of nested subalgebras and prove complete integrability. By construction, these models are integrable with respect to both Poisson structures. The eigenvalues of the Nijenhuis tensor are a choice of action variables. Our proof relies on an explicit formula for the contravariant connection defined on vector bundles that are Poisson with respect to the Bruhat-Poisson structure.
We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson ...structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.
We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained ...graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.
Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections ...if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kahler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type.
An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to ...study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction.
J.Geom.Phys.57:731-744,2007 We construct the moduli spaces associated to the solutions of equations of
motion (modulo gauge transformations) of the Poisson sigma model with target
being an integrable ...Poisson manifold. The construction can be easily extended
to a case of a generic integrable Lie algebroid. Indeed for any Lie algebroid
one can associate a BF-like topological field theory which localizes on the
space of algebroid morphisms, that can be seen as a generalization of flat
connections to the groupoid case. We discuss the finite gauge transformations
and discuss the corresponding moduli spaces. We consider the theories both
without and with boundaries.
To evaluate the accuracy of exercise two-dimensional echocardiography for the recognition of coronary artery disease, 53 patients (46 men and 7 women, age range 35 to 69 years) without either ...previous myocardial infarction or resting wall motion abnormalities, were studied. According to coronary angiography 26 had normal coronary arteries, 14 had one-vessel, seven had two-vessel, and six had three-vessel disease. After withdrawal of any therapy, all patients underwent a single exercise stress test with a stress table during which cine-loop digitized echocardiography was acquired and 74 MBq of thallium-201 (TI-201) were injected. Echocardiographic images were evaluated at rest and at peak exercise. Three-view planar scintigraphic images were collected immediately after exercise and 4 hours later. For the overall recognition of coronary artery disease, exercise electrocardiography had 77.8% sensitivity and 65.4% specificity; myocardial scintigraphy had 100% sensitivity and 92.3% specificity; and exercise echocardiography had 92.6% sensitivity and 96.2% specificity (both NS versus myocardial scintigraphy). Global accuracy was 71.7% for exercise electrocardiography, 94.3% for stress echocardiography, and 96.2% for myocardial scintigraphy. For the classification of the individual involved coronary arteries, the sensitivity of myocardial scintigraphy was 84.8% and that of exercise echocardiography was 63% (p less than 0.01); the related specificities were 98% and 98.2% respectively (NS). It may be concluded that exercise echocardiography is highly accurate for the recognition of coronary artery disease, whereas it appears less sensitive in the identification of the involved vessels, particularly in patients with multivessel disease.
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