Euclideanization of Minkowski Spacetime via Conic Projection

Evaluating integrals over the whole Minkowski spacetime, the hyperbolic domain of special relativity and quantum field theory (QFT), typically requires a Euclideanization procedure to ensure computability and convergence. Wick rotation, a rotation of the temporal axis in a complex plane, is the standard method of Euclideanization used in QFT; it is guaranteed by Cauchy’s theorem to preserve the value of the original integral for certain classes of integrals, but not all. This presentation will demonstrate a novel, geometrically-motivated Euclideanization procedure, referred to as conic projection, which avoids complexification of the time coordinate.