Complex time path for the tunnelling at intermediate energy

Abstract

The authors investigate tunnelling through a potential barrier in quantum mechanics extending Feynman's path integral to complex time paths. This problem has gained new interest in the context of baryon number violating processes in the standard electroweak model, where the transitions between topological sectors must be described at high energies and temperatures. The authors reduce the number of degrees of freedom to one in order to test their method. It is found that a path in the complex time plane consisting of purely real or imaginary steps minimizes the real and imaginary parts of the action simultaneously. Jumps from real to imaginary time increments are situated at the turning points of the classical problem. Possible extensions to field theory are discussed.