feat: bounded properties of Higgs potential

2024-09-05 18:21:43 -04:00 · 2024-09-05 18:21:43 -04:00 · 27721bc476
commit 27721bc476
parent 0dd6f7390e
4 changed files with 249 additions and 57 deletions
--- a/HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean
+++ b/HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean
@ -146,6 +146,9 @@ lemma normSq_smooth (φ : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘(ℝ,
    exact ((φ.apply_re_smooth 1).smul (φ.apply_re_smooth 1)).add $
      (φ.apply_im_smooth 1).smul (φ.apply_im_smooth 1)

+lemma ofReal_normSq {a : ℝ} (ha : 0 ≤ a) (x : SpaceTime) : (ofReal a).normSq x = a := by
+  simp only [normSq, ofReal, HiggsVec.toField_apply, ha, HiggsVec.ofReal_normSq]
+
 end HiggsField

 end StandardModel