Nichtkommutative Yang-Mills-Theorie und D-Branes

• Applicant: Dr. Bianca Letizia Cerchiai
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2000 to 2003
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5236290

My research project deals with the applications of non-commutative geometry to physical systems. Recent developments in string theory seem to suggest that the structure of space-time at very short distances could better be described in terms of a non-commutative space-time. The idea is that an action which is very complicated in the usual commutative coordinates can be expressed as a simple action in a non-commutative space, e.g. in string theory the commutative Born-Infeld action for D-branes has been proven to be equivalent to a non-commutative Yang-Mills theory. This project aims at constructing and investigating the properties of a gauge-theory on non-commutative spaces, in particular through the application of quantum groups, which are Hopf algebras providing deformations of the usual Lie-groups. This has the advantage that non-commutativity is obtained, but the symmetry structure is preserved. Noncommutativity leads to a discretization of space-time and therefore these kinds of models are automatically defined on a lattice-like structure. This should lead to a field theory which is naturally regularized because of the existence of a cut-off at short distances.

• DFG Programme: Research Fellowships
• International Connection: USA