arXiv subjects
Publications and source records attributed to M. Blau.
The BAT instrument tells the Swift satellite where to point to make immediate follow-up observations of GRBs. The science software on board must efficiently process gamma-ray events coming in at up to 34 kHz, identify rate increases that could be due to GRBs while disregarding those from known sources, and produce images to accurately and rapidly locate new Gamma-ray sources.
We give a derivation of the Verlinde formula for the $G_{k}$ WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function $Z_{Σ\times S^{1}}$ of $Σ\times S^{1}$ with an arbitrary number of labelled punctures. By a suitable gauge choice, $Z_{Σ\times S^{1}}$ is reduced to the partition function of an Abelian topological field theory on $Σ$ (a deformation of non-Abelian BF and Yang-Mills theory) whose evaluation is straightforward. This relates the Verlinde formula to the Ray-Singer torsion of $Σ\times S^{1}$. We derive the $G_{k}/G_{k}$ model from Chern-Simons theory, proving their equivalence, and give an alternative derivation of the Verlinde formula by calculating the $G_{k}/G_{k}$ path integral via a functional version of the Weyl integral formula. From this point of view the Verlinde formula arises from the corresponding Jacobian, the Weyl determinant. Also, a novel derivation of the shift $k\ra k+h$ is given, based on the index of the twisted Dolbeault complex.
These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of the Mathai-Quillen formalism for finite dimensional vector bundles; the definition of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over spaces of connections.