Lecture: Gauge
Theory and Dirac Operators ^{
}

Dirac operators play an important role in modern physics and
mathematics. Originally, this operator was introduced by P. Dirac
(1928), when looking for an equation to describe

spin 1/2 particles (fermions, e.g. electrons) that would fit into the
framework of both special relativity and quantum mechanics.

In course of the development of the index theory of elliptic
operators it was observed that it is possible to define an analogeous
operator on special Riemannian manifolds, the spin manifolds, and
that its analytical properties are strongly related to the geometry of
the Riemannina manifold. In the lecture we define the Dirac operator of
a Riemannian spin manifold and study its analytic properties in
relation to the underlying geometry.

The definition and the study of spinors and Dirac operators on
Riemannian spin manifolds require knowledge from differential geometry
on fibre bundles. Depending on the prior knowledge of the participants
we will introduce or recall the techniques and facts from gauge theory
in the first part of the lecture.

Literature:

T. Friedrich: Dirac Operators in Riemannian Geometry, . AMS 2000.

J-P. Bourguignon et all: A Spinorial Approach to Riemannian and Conformal Geometry, EMS Monographs in Mathematics 2015

N. Ginoux: The Dirac spectrum. Lecture Notes in Math., Springer 2009

Lecture: Thusday 09:15 - 10:45, room RUD 26, 0311

Wednesday 13:15 - 14:45, room RUD 26, 0311

exercise class: Thusday 11:15 - 12:45, room RUD 25, 2.006

Exam:

The date for the oral exam follows.

Letzte Änderung: 11.04.2017