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refactor: Start refactoring potential of Higgs field

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jstoobysmith 2024-09-12 09:23:43 -04:00
parent 2c257eb4c0
commit 2f4b9bc627
3 changed files with 306 additions and 3 deletions
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5
HepLean/StandardModel/HiggsBoson/GaugeAction.lean
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@ -169,12 +169,11 @@ theorem rotate_fst_real_snd_zero (φ : HiggsVec) :
∃ (g : GaugeGroup), rep g φ = ![Complex.ofReal ‖φ‖, 0] := by
obtain ⟨g, h⟩ := rotate_fst_zero_snd_real φ
let P : GaugeGroup := ⟨1, ⟨!![0, 1; -1, 0], by
rw [@mem_specialUnitaryGroup_iff]
rw [mem_specialUnitaryGroup_iff]
apply And.intro
· rw [mem_unitaryGroup_iff, star_eq_conjTranspose]
ext i j
rw [Matrix.mul_apply]
rw [@Fin.sum_univ_two]
rw [Matrix.mul_apply, Fin.sum_univ_two]
fin_cases i <;> fin_cases j
<;> simp
· simp [det_fin_two]⟩, 1⟩