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Published equation contexts

ΓV=A e−SE\frac{\Gamma}{V} = A\,e^{-S_E}

Why this formula appears here

If the electroweak vacuum is a local minimum rather than the global one, then in a quantum theory it is not perfectly stable; it can, in principle, decay by quantum tunneling to a lower-energy configuration, a possibility with no analogue in classical statistical mechanics. Coleman’s 1977 paper “Fate of the false vacuum” put the semiclassical machinery for this process on rigorous footing, treating decay as bubble nucleation: a small region of true vacuum appears through tunneling, and if the bubble is large enough that the volume energy released by the lower-energy interior outweighs the surface energy cost of the wall separating it from the surrounding false vacuum, the bubble expands,…

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VV

Symbol V

V occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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e−SEe^{-S_E}

Symbol e^-S_E

e−e^-SES_E is one of the signed contributions combined to compute the quantity on the left.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

ΓV=A e−SE,\frac{\Gamma}{V} = A\,e^{-S_E},

Equation 11 · Evolutionary Physics

The Vacuum Has a History: Symmetry Breaking as Speciation

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

If the electroweak vacuum is a local minimum rather than the global one, then in a quantum theory it is not perfectly stable; it can, in principle, decay by quantum tunneling to a lower-energy configuration, a possibility with no analogue in classical statistical mechanics. Coleman’s 1977 paper “Fate of the false vacuum” put the semiclassical machinery for this process on rigorous footing, treating decay as bubble nucleation: a small region of true vacuum appears through tunneling, and if the bubble is large enough that the volume energy released by the lower-energy interior outweighs the surface energy cost of the wall separating it from the surrounding false vacuum, the bubble expands,…

Meanings in this article

  • AA: a prefactor from fluctuations around that solution.
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