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This project is inspired by the idea that black holes could explode due to a quantum process somewhat analogous to quantum mechanical tunneling. This idea was presented in recent research that also proposed that semiclassical physics could be used to investigate the so called black hole fireworks. Semiclassical physics connects quantum and classical physics and because of this it is a powerful tool for investigating gravity where the classical theory is known but there is no complete quantum theory. Unfortunately, the traditional tools in semiclassics that are needed fail to treat tunneling. However, if classical mechanics is extended to complex rather than real values, tunneling-like phenomenon can be recovered. This project investigates classical mechanics when it is extended to complex values and how this relates to semiclassics. The project provides background information on analytic continuation, Riemann surfaces, and semiclassical physics. It addresses complex classical mechanics, complex semiclassics, and ends by setting up the gravity calculation. The focus of the project is on three example problems where complex trajectories are used to find the quantum mechanical propagator.
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Meynig, Max Edward, "Complex Semiclassics: Classical Models for Tunneling Using Complex Trajectories" (2016). Senior Projects Spring 2017. 243.