In-in formalism on tunneling background: Multidimensional quantum mechanics

Abstract

We reformulate quantum tunneling in a multidimensional system where the tunneling sector is nonlinearly 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.