This is for example the case in the current quantum field explanation of mass of elementary particles in the framework of the Standard Model, the Higgs mechanism.
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The complete formulation of the standard model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations suggest that the standard model is incomplete.
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Then if the mass term is tachyonic, m ^ 2 there is a spontaneous breaking of the gauge symmetry at low energies, a variant of the Higgs mechanism.
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But historically, a model similar to this ( but not using the Higgs mechanism ) was the first in which the weak force and the electromagnetic force were unified.
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The Higgs mechanism, Hawking Radiation and the Unruh effect are also theorized to be dependent on zero-point vacuum fluctuations, the field contribution being an inseparable parts of these theories.
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In condensed matter physics a notable example is ferromagnetism; in particle physics the best known example is the Higgs mechanism in the standard model that breaks the electroweak symmetry.
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When turning to a Yang Mills theory with spontaneous symmetry breaking due to the Higgs mechanism, one finds that BPST instantons are not exact solutions to the field equations anymore.
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Most of those fields are believed to be massless at high enough energies, but at low energies, after electroweak symmetry breaks, many of them acquire mass through the Higgs mechanism.
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His primary research interest is physics beyond the standard model with particular focus on the Higgs mechanism and potentially related physics such as supersymmetry, new forces, extra dimensions and dark matter.
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:The Higgs field ought to have a vacuum energy density ( which would act like dark energy ), and it ought I suppose to be negative given how the Higgs mechanism works.
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