Geometry and Gauge TheoryAnnouncements (new ones first)
SummaryThe course will start with a geometric discussion of Hamiltonian systems with so-called second and first class constraints. The latter are related to local symmetries (gauge symmetries). Explicitly solving the constraints usually breaks covariance under the symmetry groups of the system. This can be avoided by setting the constraints to zero only cohomologically. There will be two differentials with a clear geometrical meaning, the Koszul Tate differential and the longitudinal exterior derivative , whose relative cohomology will provide the physical subspace. The same can be obtained in a single step, by combining the two to the so-called BRST-differential.Also the corresponding machinery in the Lagrangian formalism will be discussed. It is known under the names "antifield-formalism" or "BV formalism" and is based on an odd bracket, the "antibracket" (which is a Gerstenhaber bracket). The discussions will be first at classical level. However, an important motivation for the cohomological description of gauge symmetries is the task of covariantly quantizing a theory. We will thus continue to discuss quantum corrections as well as anomalies. The formalism will be applied in particular to Yang Mills theory whose fibre bundle geometry is also one of the main topics. It is rather improbable that we will make it through the whole list of topics sketched at the fenix-announcement of this course. We will see, how much time will be left and then choose among the remaining subjects depending on your, but in particular also on my preference ;-) Please note that at present I have no possibility to edit the content on the fenix-site myself, so all new announcements will be done on this website here. However, rough summaries of the previous lectures are announced by now on the fenix site. Bibliography
For further information please drop me an email (don't forget to delete the capital letters in the email-address) or step by (office 2.09 in the math building). |