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High Energy Physics - Theory, hep-th,Quantum Physics, quant-ph
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.
