On the global solutions of the Higgs boson equation
Karen Yagdjian
TL;DR
This paper investigates the behavior of global solutions to the Higgs boson equation in Minkowski and de Sitter spacetimes, providing conditions for zero creation and oscillatory behavior relevant to physics and cosmology.
Contribution
It offers new qualitative insights and sufficient conditions for zero creation and oscillations of solutions to the Higgs boson equation in different spacetime models.
Findings
Conditions for zeros of solutions in their supports
Criteria for oscillatory solutions in time
Analysis applicable to particle physics and cosmology
Abstract
In this article we study global in time (not necessarily small) solutions of the equation for the Higgs boson in the Minkowski and in the de Sitter spacetimes. We reveal some qualitative behavior of the global solutions. In particular, we formulate sufficient conditions for the existence of the zeros of global solutions in the interior of their supports, and, consequently, for the creation of the so-called bubbles, which have been studied in particle physics and inflationary cosmology. We also give some sufficient conditions for the global solution to be an oscillatory in time solution.
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