← All parts of this equation

Equation 5 · Part 2 · The Vacuum Has a History: Symmetry Breaking as Speciation

Symbol mu

∣ϕ∣=μ/2λ|\phi| = \mu/\sqrt{2\lambda}
μ\mu

What this part means

mu is an input to the expression that computes the quantity on the left.

Its job in the formula

mu is an input to the expression that computes the quantity on the left.

The passage around this formula

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 of the mass term is the entire mechanism. With μ2\mu^2 < 0 the origin would be the unique minimum and there would be nothing to discuss; it is the negative mass-squared term, an assumption built into the Standard Model’s Higgs sector rather than derived from a deeper principle, that manufactures the trough in the first place. Nothing in the Lagrangian singles out any point on that trough. A system placed at the unstable summit will roll downhill in a direction fixed…

Read this part in the article →

Learn the underlying idea

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.