Alternative techniques for Minkowski spacetime integration

Integration over Minkowski spacetime, an inevitable ingredient of quantum field theory, necessitates use of special techniques such as Wick rotation, in which the practitioner rotates their time axis in the complex plane. Despite its convenience, this procedure lacks physical motivation and, further, while the integration measures are Lorentz-invariant, there is no Lorentz transformation equivalent to a Wick rotation. Recently, a fresh perspective on Lorentz transformations emerged in the form of Renormalized Blended Spacetime (RBS) coordinates that cleverly map from hyperbolic Minkowski spacetime to a flat Euclidean space, accomplished by first "blending" measurements of a single event made in two frames that are separated by a boost and then "renormalizing" such that the magnitude of the spacetime interval is left unchanged. (Note that this, despite redundant nomenclature, is distinct from the usual renormalization performed in QFT.) This presentation will outline two alternative methods, based on RBS coordinates, for computing spacetime integrals without the use of Wick rotation.