Fun with Path Integrals

Feynman's path integral provides an elegant formulation of quantum physics, particularly suited to theories with continous symmetries, like gauge theories and general relativity. However, it has proven difficult to rigorously define path integrals without first performing a Wick rotation to Euclidean time. Unfortunately, this significantly compromises the study of quantum dynamics, particularly in the nonperturbative regime. We have been developing a new approach to Lorentzian (i.e. non-Wick-rotated) path integrals, which allows us to define and calculate real spacetime amplitudes for quantum fields and particles and gravity. Surprising applications so far include quantum cosmology (for example, Hartle and Hawking's famous no boundary proposal) and strong interference effects in radio astronomy - literally, path integrals in the sky!