Developments in 3D representations and Local Unitarity - Zeno Capatti (Bern)

In this talk, I will review the derivation and theoretical properties of the Loop Tree Duality, Time-Ordered Perturbation Theory, and Cross-Free Family representations (3D representations) of loop integrals, as well as how they can be used to numerically compute Feynman diagrams relevant for collider precision physics, for finite-density and finite-temperature QCD calculations, for non-relativistic condensed matter many-body systems, and for black-hole scattering observables. I will also review a little-known on-shell relation based on the Loop Tree Duality representation and discuss possible future uses of it. Finally, I will discuss how 3D representations naturally lead to the Local Unitarity formalism, which combines real and virtual contributions to a differential cross-sections at the integrand level, allowing for the KLN cancellation of infrared singularities to take place locally. I will briefly explore implications of the KLN theorem and Local Unitarity for the cancellation of initial-state singularities, focusing on including the effect of multi-partonic initial states in calculations related to the Deep Inelastic Scattering process.