Numerical Lattices and Quantum Electrodynamic Bound-State Calculations

An accurate understanding of the Green functions of bound systems is of crucial importance for the calculation of quantum-electrodynamic corrections in bound systems. Traditionally, the so-called Sturmian decomposition of the hydrogen Green function has been used to good effect in semi-analytic calculations of relativistic quantum-electrodynamic calculations. However, for highly excited (Rydberg) reference states, an excessively large number of terms is generated in intermediate steps, so large in fact that even modern computer-algebra systems are overwhelmed. A solution is provided by exponential numerical lattices where the problem is mapped onto an exponentially distributed set of radial points. The advantages are numerous. For example, the treatment of vacuum-polarization induced corrections to Bethe logarithms in muonic bound systems is drastically simplified on a numerical lattice. The calculations are used in order to search for New Physics in upcoming experiments; a brief overview will be provided.