$1/\epsilon$ problem in resurgence

Abstract

Abstract This paper considers the $1/\epsilon$ problem, which is the divergent behavior of the ground-state energy of the asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and the resurgence technique. Using the resolvent method, it is shown that including not only one complex bion but a multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle-point contributions and also the relationship between the exact Wentzel–Kramers–Brillouin approximation and path-integral formalism.