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Quantum State during and after the False Vacuum Decay
The transition of a quantum state associated with the false vacuum decay of a metastable system is investigated based on the WKB wave functional approach. In a covariant manner, we reformulate the WKB wave function for a multidimensional tunneling system with finite degrees of freedom, which describes the quasi-ground state of the svstem. Then we extend the formalism to the case of a field theory and develop a systematic method to construct the wave functional which determines the quantum state after the false vacuum decay. A clear interpretation of the resulting quantum state is given in the language of the conventional second quantized picture. Using this formalism, we investigate the quantum state during and after the nucleation of an O(4)-symmetric bubble. We find that the quantum state inside the nucleated bubble is Lorentz-invariant but very different from the Minkowski vacuum. There exists a family of hypersurfaces oil which the energy density is constant as a consequence of the invariance of the state, and the expectation value of the energy momentum tensor behaves like radiation. Then we find the possilility of creating a homogeneous and isotropic open universe through the nucleation of an O(4)-symmetric bubble. To extend this investigation to more general cases, we study tunneling phenmenon in simple quantum mechanical svstems with emphasis on the interaction between the tunneling mode and that coupled to it. Analysis using the WKB wave function shows that the energy is transferred to the tunneling mode, and implication to a false vacuum clecay in the presence of field excitations before the tunneling is discussed.
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