New Methods for the Calculation of Multi-Loop Amplitudes

In the era of the LHC and in preparation for the ILC there is need for multi-loop calculations to match the precision of these experiments from the theory side. The classes of problems currently accessible reach from multi-leg multi-scale problems at one-loop up to no-scale propagator, and tadpole diagrams at four-loop level. Many problems fall into these categories directly while others can be cast into the required form by appropriate expansions in small parameters. A typical multi-loop calculation proceeds as follows: The needed diagrams are generated and if necessary expanded to decrease the difficulty of the problem. The resulting Feynman integrals are then reduced to a small set of simpler integrals, which have to be calculated in a further step. While the reduction of the integrals can be automatized completely and is mostly independent of the problem at hand, the calculation of the remaining integrals must still be done manually for every calculation. In the following we give a brief review of the current status of the reduction to master integrals which with recent developments is now in a good shape such that the calculation of the master integrals now again poses the most difficulties in multi-loop calculations.