Research proof index

Two gauge elements induce the same action exactly when their hypercharge–colour coefficients agree.

Expands the gauge action in the spinor–colour basis.

The part of a potential at a given mass-dimension. -/ def termOfMassDim (V : EffectivePotential) {n : ℕ} (h : HasMaxMassDimLE V n) (m : ℕ) : HiggsVec → ℝ := fun φ => ((polynomial V h).homogeneousComponent m).eval φ.toRealScalars lemma termOfMassDim_eq_zero_of_max_lt {V : EffectivePotential} {n : ℕ} (h : HasMaxMassDimLE V n) {m : ℕ} (hm : n < m) (φ : Higgs...

Given a element P of Potential which is bounded, the quartic coefficient 𝓵 of P is non-negative.

For an element P of Potential with l < 0 and a real c : ℝ, there exists a Higgs field φ and a spacetime point x such that P.toFun φ x = c iff one of the following two conditions hold: - 0 < μ2 and c ≤ 0. That is, if l is negative and μ2 positive, then the potential takes every non-positive value. - or μ2 ≤ 0 and `c ≤ - μ2 ^ 2 / (4...

The Higgs potential is zero iff and only if the higgs field is zero, or the higgs field has norm-squared P.μ2 / P.𝓵, assuming P.𝓁 = 0.