Negative Dimensional Integration for Massive Four Point Functions–i: the Standard Solutions

Feynman diagrams are the best tool we have to study perturbative quantum field theory. For this very reason the development of any new technique which allows us to compute Feynman integrals is welcome. By the middle of the 80’s, Halliday and Ricotta suggested the possibility of using negative dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such and check up on its possibilities. For this purpose, we take a box diagram integral contributing to the photon-photon scattering amplitude in quantum electrodynamics using the negative dimensional integration method. The reason for this choice of ours is twofold: Firstly, it is a well-studied integral with well-known results, and secondly because it bears in its integrand the complexities associated with four massive propagators of the intermediate states.