In-in formalism on tunneling background: multi-dimensional quantum mechanics

TL;DR

This paper develops a formalism for multi-dimensional quantum tunneling with non-linear couplings, explicitly constructing the wave function and connecting it to the in-in formalism, with potential cosmological implications.

Contribution

It introduces a reformulation of multi-dimensional tunneling using the in-in formalism, explicitly constructing the wave function in such systems.

Findings

Explicit construction of the WKB wave function in multi-dimensional tunneling

Connection of post-tunneling quantum states to the in-in formalism

Discussion of implications for cosmological models

Abstract

We reformulate quantum tunneling in a multi-dimensional system where the tunneling sector is non-linearly coupled to oscillators. The WKB wave function is explicitly constructed under the assumption that the system was in the ground state before tunneling. We find that the quantum state after tunneling can be expressed in the language of the conventional in-in formalism. Some implications of the result to cosmology are discussed.