A Local Index Formula for the Quantum Sphere
نویسندگان
چکیده
For the Dirac operatorD on the standard quantum sphere we obtain an asymptotic expansion of the SUq(2)-equivariant entire cyclic cocycle corresponding to ε 1 2D when evaluated on the element k ∈ Uq(su2). The constant term of this expansion is a twisted cyclic cocycle which up to a scalar coincides with the volume form and computes the quantum as well as the classical Fredholm indices.
منابع مشابه
An integrated Assessment System of Citizen Reaction towards Local Government Social Media Accounts
Agovernmentshouldusesocialmediaforcommunicatingwithitscitizen.Theengagement index score is one of the methods for assessing the rate of governmental success in using social media as a tool in establishing interactive relationships with its citizen. In general, the engagement index score is obtained by calculating the number of posts, number of likes and comments, and so forth on a single social...
متن کاملمحاسبه پتانسیل برهمکنش واندروالس گرمایی با استفاده از پتانسیل کازیمیر- پولدر
In this study, thermal Casimir-Polder potential is calculated for an atom in the presence of a dielectric sphere using the formula given in terms of the Green’s function. Then, the limiting cases of large and small sphere are investigated. In the limiting case of a large sphere, the formula of thermal potential for an excited atom in the presence of a dielectric half-space and then a perfectly ...
متن کاملAn Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let (V, 0) be a germ of a complete intersection variety in C, n > 0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on C tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space C we give a formula for the homological in...
متن کاملLocal Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure
We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...
متن کاملLiouville Quantum Gravity on the Riemann sphere
In this paper, we rigorously construct 2d Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov Quantum Geometry of bosonic strings. We also establish some of its fundamental properties like conformal covariance under PSL2(C)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quant...
متن کامل