Tunneling Hamiltonian representation of false vacuum decay I. Comparison with the Bogomil'nyi inequality

Abstract

The tunneling Hamiltonian has proven to be a useful method in many body physics to treat particle tunneling between different states represented as wave functions. Here we present a generalization of the tunneling Hamiltonian to quantum field theory, in which tunneling between states represented as wave functionals of a scalar quantum field is considered. We examine quantum decay of the false vacuum in the driven Sine-Gordon system, and show it is consistent with the tunneling formalism derived here and matches up with the soliton - anti soliton separation obtained from the Bogomil'nyi inequality. This inequality permits construction of a gaussian wave functional representation of soliton - anti soliton nucleated states and is consistent with respect to the false vacuum hypothesis