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Equation 2 · Part 2 · The Vacuum Has a History: Symmetry Breaking as Speciation

Symbol phi

V(ϕ)=−μ2 ϕ†ϕ+λ (ϕ†ϕ)2,μ2>0, λ>0.V(\phi) = -\mu^2\,\phi^\dagger\phi + \lambda\,(\phi^\dagger\phi)^2, \qquad \mu^2 > 0,\ \lambda > 0.
ϕ\phi

What this part means

phi is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

phi is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

The simplest version of the mechanism starts from a single complex scalar field ϕ\phi with a potential energy density of the form V(ϕ)=−μ2 ϕ†ϕ+λ (ϕ†ϕ)2,μ2>0, λ>0V(\phi) = -\mu^2\,\phi^\dagger\phi + \lambda\,(\phi^\dagger\phi)^2, \qquad \mu^2 > 0,\ \lambda > 0. Plotted against the two real components of ϕ\phi , this is the shape popularly called the Mexican hat: a local maximum at ϕ\phi = 0 , surrounded by a circular trough of degenerate minima at |ϕ\phi| = μ\mu/2λ\sqrt{2\lambda} . The sign…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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