Mechanisms for Gauge Symmetry Breaking and Fermion Masses Generation

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The problem of mass generation for elementary particles is far from being understood. There are two different mass generating mechanisms in the electroweak standard model: the Higgs mechanism generates a mass for the electroweak bosons and the Yukawa interactions allow to implement masses for fermions in the model. This implies that the model contains many free parameters that cannot be computed from first principles. Grand unified theories (GUTs) allow to reduce the number of fundamental parameters. Furthermore the Higgs mechanism seems to be an effective theory. The goals of this project are the following: 1) to find alternatives to the Higgs mechanism and in particular to find dynamical mechanisms that trigger the Higgs mechanism; 2) to implement these mechanisms in GUTs and to derive the consequences for fermion masses; 3) to propose tests of GUTs if the fundamental parameters of the theory have a cosmological time evolution; 4) to study the implications of a possible noncommutative nature of space-time for the masses of the fermions and of the gauge bosons.