NEGATIVE-DIMENSIONAL INTEGRATION REVISITED

Feynman diagrams are the best tool we have to study perturbative quant um field theory. For this very reason the development of any new techn ique that allows us to compute Feynman integrals is welcome. By the mi ddle of the 1980s, Halliday and Ricotta suggested the possibility of u sing negative-dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such and check on its possibi lities. For this purpose, we take a box diagram integral contributing to the photon-photon scattering amplitude in quantum electrodynamics u sing the negative-dimensional integration method. Our approach enables us to quickly reproduce the known results as well as six other soluti ons as yet unknown in the literature. These six new solutions arise qu ite naturally in the context of negative-dimensional integration metho d, revealing a promising technique to handle Feynman integrals.