The Geometric Calculus of Variations and its Applications
(ERC Advanced Investigator Grant)
Jürgen Jost (Email)
+49 (0) 341 - 9959 - 552
+49 (0) 341 - 9959 - 658
Variational problems, QFT, Symmetries and applications:
On the set of all Dirac operators there exists a natural functional, called ``Dirac functional''. When restricted to specific subsets of Dirac operators, the Dirac functional reduces to functionals well-known in geometry and physics, like the Einstein-Hilbert and the the Yang-Mills functional. Also the functional of what is called the ``Standard Model'' in high-energy physics can be geometrically described this way in terms of a certain subset of Dirac operators. This motivates to systematically classify Dirac operators and its underlying Clifford modules. This may become especially fascinating when related to supersymmetry.