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

We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter-space for the initial conditions. In order to construct the field theory around th...

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Bibliographic Details
Published in:arXiv.org 2015-12
Main Authors: Kitadono, Yoshio, Inagaki, Tomohiro
Format: Article
Language:English
Subjects:
Equations of motion
Field theory
Initial conditions
Jacobian elliptic functions
Perturbation methods
Perturbation theory
Quantum phenomena
Quantum theory
Transition probabilities
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Summary:We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter-space for the initial conditions. In order to construct the field theory around the oscillating solutions quantum fluctuations are introduced. This alternative perturbation method is useful to describe the non-trivial quantum theory around the oscillating state. This perturbation theory reduces to the standard one if we take the solution at the vacuum expectation value. It is shown that the transition probability between the vacuum and multi-quanta states is finite as long as the initial field configuration does not start from the true vacuum.
ISSN:2331-8422
DOI:10.48550/arxiv.1512.08123