Negative mode problem of false vacuum decay revisited

Abstract

We study negative modes around the Coleman-de Luccia bounce solution. The conditions for the appearance of an infinite number of negative modes do not coincide between Lagrangian and Hamiltonian formulations in the literature, and we discuss the origin of this difference in detail. We show how different choices of the variable for the fluctuation around the bounce solution affect the negative mode condition in the Hamiltonian approach, and point out that there exists a choice that gives the same ive mode condition as the Lagrangian approach.