One-Loop Amplitudes in Perturbative Quantum Field Theory
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We review methods for calculation of higher order corrections in perturbative quantum field theory. After laying the foundation with several traditional methods we turn to more recent developments. A particular method, proposed by Ossola, Papadopoulos and Pittau, reduces tensor integrals from one-loop diagrams with many external particles to known scalar integrals. This is achieved by a highly efficient algebraic algorithm, thereby opening the window to more precise predictions for collider processes. We describe the method and present an algebraic implementation in FORM. In the field of soft corrections, some spectacular progress has been made as well. Processes can be calculated to all orders in perturbation theory through exponentiation of a certain set of diagrams. We investigate properties of such diagrams by applying the unitarity method.