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