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

Understand

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.