Group of Rainer Häußling

Members: R. Häußling

Research interests

Noncommutative Geometry Models and Quantization

Despite its undeniable success when confronted with experiment, the Standard Model of
particle physics definitely falls short of being a complete theory of fundamental interactions.
Apart from the fact that gravity is not incorporated at all, the Standard Model exhibits
too much arbitrariness in order to be accepted as a really fundamental theory from a
theoretical point of view.
During the last 15 years a number of possible solutions to some of the more qualitative
defects of the Standard Model such as the origin of masses, the origin of generation mixing
and the assignment of quantum numbers have been proposed, these solutions having their
roots in Noncommutative Geometry (NCG). All these NCG based models are at first
formulated at the classical level, and quantization is subsequently accomplished by
applying common pratices thereby disregarding the initial and promising noncommutative
framework. Hence tracking down an adequate quantization procedure that takes into
account the noncommutative setting seriously is not only of central interest but
undoubtedly would be an essential step towards a noncommutative theory of fundamental
interactions which bears its name rightly. Because of the complexity of the problem in a
first attempt NCG toy models with a manageable number of degrees of freedom are
investigated.


Reconstruction of Mass Matrices

The Mainz-Marseille-model of electroweak interactions, ranking among the NCG models,
suggests a specific, though general pattern for the mass matrices of quarks and leptons
which allows for an economic reconstruction of the entries of the mass matrices in terms
of experimental data. The objective of such an analysis consists in unveiling possible
structures within the mass matrices which in turn could possibly point to physics beyond
the Standard Model.


Renormalization of Quantum Field Theories

On the one hand the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization
scheme is characterized by conceptual clarity, but on the other hand this scheme proves
to be unqualified in concrete calculations. Thus the question arises whether it is possible
to modify the BPHZ scheme in such a way that its vantages survive while simultaneously
its disadvantages reduce.