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refactor: Spellings

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jstoobysmith 2025-02-08 13:07:54 +00:00
parent 4cd71f5ec6
commit 4a55351b72
33 changed files with 88 additions and 88 deletions
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14
HepLean/StandardModel/HiggsBoson/GaugeAction.lean
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@ -118,7 +118,7 @@ lemma rotateMatrix_det {φ : HiggsVec} (hφ : φ ≠ 0) : (rotateMatrix φ).det
simp [PiLp.inner_apply, Complex.inner, neg_mul, sub_neg_eq_add,
Fin.sum_univ_two, ofReal_add, ofReal_mul, mul_conj, mul_comm, add_comm]
/-- The `rotateMatrix` for a non-zero Higgs vector is untitary. -/
/-- The `rotateMatrix` for a non-zero Higgs vector is unitary. -/
lemma rotateMatrix_unitary {φ : HiggsVec} (hφ : φ ≠ 0) :
(rotateMatrix φ) ∈ unitaryGroup (Fin 2) ℂ := by
rw [mem_unitaryGroup_iff', rotateMatrix_star, rotateMatrix]
@ -148,15 +148,15 @@ lemma rotateMatrix_specialUnitary {φ : HiggsVec} (hφ : φ ≠ 0) :
/-- Given a Higgs vector, an element of the gauge group which puts the first component of the
vector to zero, and the second component to a real number. -/
def rotateGuageGroup {φ : HiggsVec} (hφ : φ ≠ 0) : GaugeGroupI :=
def rotateGaugeGroup {φ : HiggsVec} (hφ : φ ≠ 0) : GaugeGroupI :=
⟨1, ⟨(rotateMatrix φ), rotateMatrix_specialUnitary hφ⟩, 1⟩
/-- Acting on a non-zero Higgs vector with its rotation matrix gives a vector which is
zero in the first component and a positive real in the second component. -/
lemma rotateGuageGroup_apply {φ : HiggsVec} (hφ : φ ≠ 0) :
rep (rotateGuageGroup hφ) φ = ![0, Complex.ofRealHom ‖φ‖] := by
lemma rotateGaugeGroup_apply {φ : HiggsVec} (hφ : φ ≠ 0) :
rep (rotateGaugeGroup hφ) φ = ![0, Complex.ofRealHom ‖φ‖] := by
rw [rep_apply]
simp only [rotateGuageGroup, rotateMatrix, one_pow, one_smul,
simp only [rotateGaugeGroup, rotateMatrix, one_pow, one_smul,
Nat.succ_eq_add_one, Nat.reduceAdd, ofRealHom_eq_coe]
ext i
fin_cases i
@ -184,8 +184,8 @@ theorem rotate_fst_zero_snd_real (φ : HiggsVec) :
norm_zero]
ext i
fin_cases i <;> rfl
· use rotateGuageGroup h
exact rotateGuageGroup_apply h
· use rotateGaugeGroup h
exact rotateGaugeGroup_apply h
/-- For every Higgs vector there exists an element of the gauge group which rotates that
Higgs vector to have `0` in the second component and be a non-negative real in the first