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We investigate oscillating solutions of the equation of motion for the Higgspotential. The solutions are described by Jacobian elliptic functions.Classifying the classical solutions, we evaluate a possible parameter-space forthe initial conditions. In order to construct the field theory around theoscillating solutions quantum fluctuations are introduced. This alternativeperturbation method is useful to describe the non-trivial quantum theory aroundthe oscillating state. This perturbation theory reduces to the standard one ifwe take the solution at the vacuum expectation value. It is shown that thetransition probability between the vacuum and multi-quanta states is finite aslong as the initial field configuration does not start from the true vacuum.

Elliptically Oscillating Classical Solution in Higgs Potential and the Effects on Vacuum Transitions