Geometrical approach to causality in multi-loop amplitudes

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An impressive effort is being placed in order to develop new strategies that allow an efficient computation of multi-loop multi-leg Feynman integrals and scattering amplitudes, with a particular emphasis on removing spurious singularities and numerical instabilities.

• In this article, we describe an innovative geometric approach based on graph theory to unveil the causal structure of any multi-loop multi-leg amplitude in Quantum Field Theory.
• Our purely geometric construction reproduces faithfully the manifestly causal integrand-level behaviour of the Loop-Tree Duality representation.
• We found that the causal structure is fully determined by the vertex matrix, through a suitable definition of connected partitions of the underlying diagrams.