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Abstract

We study quantum mechanical tunneling using complex solutions of the classical field equations. Simple visualization techniques allow us to unify and generalize previous treatments, and straightforwardly show the connection to the standard approach using Euclidean instanton solutions. We demonstrate that the negative modes of solutions along various contours in the complex time plane reveal which paths contribute to tunneling and which do not, and we provide a criterion for identifying the negative modes. Central to our approach is the solution of the background and perturbation equations not only along a single path, but over an extended region of the complex time plane. Our approach allows for a fully continuous and coherent treatment of classical evolution interspersed by quantum tunneling events, and is applicable in situations where singularities are present and also where Euclidean solutions might not exist.