Event

Interference is one of the most universal phenomena in nature, as exemplified by the real-time Feynman path integral. Despite the ubiquity of interference patterns, their evaluation has often proven challenging. The oscillatory integrals involved are frequently conditionally convergent, converge slowly, and artefacts such as dependence on unphysical cut-offs can be difficult to avoid. 

 

Using Picard-Lefschetz theory—a general, exact method for handling multidimensional oscillatory integrals based on saddle point techniques—I will present strategies for efficiently defining and evaluating multidimensional oscillatory integrals in the complex plane. I will apply this technique to lens systems in wave optics, demonstrate how these principles may yield a mathematically rigorous definition of the real-time path integral in terms of relevant complex classical paths, and propose an efficient method for numerically evaluating real-time path integrals. I will briefly discuss its application in quantum cosmology when modeling the Big Bang.