Thin-shell instanton tunneling: something-to-something or nothing-to-something?

TL;DR

This paper explores two interpretations of instantons in quantum tunneling, demonstrating their complementarity and consistency between Euclidean and Hamiltonian approaches, with implications for the information loss problem.

Contribution

It clarifies the relationship between two instanton interpretations and shows their consistency, supporting their use in addressing the information loss problem.

Findings

The two instanton interpretations are complementary under certain conditions.

Euclidean and Hamiltonian decay rates are consistent.

Supports instantons as tools for the information loss problem.

Abstract

There exist two interpretations of instantons in the literature. The first interpretation regards instanton as divider between the initial and final hypersurfaces. The Coleman-De Luccia instanton is one such an example. The second interpretation, proposed by Brown and Weinberg, considers instanton as connector between the initial and final hypersurfaces. In this proceedings, we try to suitably and intuitively argue that these two interpretations are complementary to each other under certain conditions. Furthermore, we demonstrate that the decay rate obtained from the Euclidean treatment and the Hamiltonian treatment both are consistent with each other, which may help to dissolve some concerns about the validity of regularization technique employed in the treatment of the cusp singularity of instantons. Based on these, we argue that instantons can be a sensible tool to address the information loss problem.