Refactor: Names
This commit is contained in:
jstoobysmith
parent
ff89c3f79d
commit
490ed0380c
6 changed files with 342 additions and 442 deletions
|
|
@ -16,7 +16,7 @@ open CKMMatrix
|
|||
noncomputable section
|
||||
|
||||
-- to be renamed stanParamAsMatrix ...
|
||||
def standardParameterizationAsMatrix (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) : Matrix (Fin 3) (Fin 3) ℂ :=
|
||||
def standParamAsMatrix (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) : Matrix (Fin 3) (Fin 3) ℂ :=
|
||||
![![Real.cos θ₁₂ * Real.cos θ₁₃, Real.sin θ₁₂ * Real.cos θ₁₃, Real.sin θ₁₃ * exp (-I * δ₁₃)],
|
||||
![(-Real.sin θ₁₂ * Real.cos θ₂₃) - (Real.cos θ₁₂ * Real.sin θ₁₃ * Real.sin θ₂₃ * exp (I * δ₁₃)),
|
||||
Real.cos θ₁₂ * Real.cos θ₂₃ - Real.sin θ₁₂ * Real.sin θ₁₃ * Real.sin θ₂₃ * exp (I * δ₁₃),
|
||||
|
|
@ -27,10 +27,10 @@ def standardParameterizationAsMatrix (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ)
|
|||
|
||||
open CKMMatrix
|
||||
|
||||
lemma standardParameterizationAsMatrix_unitary (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
||||
((standardParameterizationAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃)ᴴ * standardParameterizationAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃) = 1 := by
|
||||
lemma standParamAsMatrix_unitary (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
||||
((standParamAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃)ᴴ * standParamAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃) = 1 := by
|
||||
funext j i
|
||||
simp only [standardParameterizationAsMatrix, neg_mul, Fin.isValue]
|
||||
simp only [standParamAsMatrix, neg_mul, Fin.isValue]
|
||||
rw [mul_apply]
|
||||
have h1 := exp_ne_zero (I * ↑δ₁₃)
|
||||
fin_cases j <;> rw [Fin.sum_univ_three]
|
||||
|
|
@ -87,17 +87,19 @@ lemma standardParameterizationAsMatrix_unitary (θ₁₂ θ₁₃ θ₂₃ δ
|
|||
rw [sin_sq, sin_sq]
|
||||
ring
|
||||
|
||||
def sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) : CKMMatrix :=
|
||||
⟨standardParameterizationAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃, by
|
||||
def standParam (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) : CKMMatrix :=
|
||||
⟨standParamAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃, by
|
||||
rw [mem_unitaryGroup_iff']
|
||||
exact standardParameterizationAsMatrix_unitary θ₁₂ θ₁₃ θ₂₃ δ₁₃⟩
|
||||
exact standParamAsMatrix_unitary θ₁₂ θ₁₃ θ₂₃ δ₁₃⟩
|
||||
|
||||
lemma sP_cross (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
||||
[sP θ₁₂ θ₁₃ θ₂₃ δ₁₃]t = (conj [sP θ₁₂ θ₁₃ θ₂₃ δ₁₃]u ×₃ conj [sP θ₁₂ θ₁₃ θ₂₃ δ₁₃]c) := by
|
||||
namespace standParam
|
||||
lemma cross_product_t (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
||||
[standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃]t =
|
||||
(conj [standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃]u ×₃ conj [standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃]c) := by
|
||||
have h1 := exp_ne_zero (I * ↑δ₁₃)
|
||||
funext i
|
||||
fin_cases i
|
||||
· simp only [tRow, sP, standardParameterizationAsMatrix, neg_mul, exp_neg,
|
||||
· simp only [tRow, standParam, standParamAsMatrix, neg_mul, exp_neg,
|
||||
Fin.isValue, cons_val', cons_val_zero, empty_val', cons_val_fin_one, cons_val_two, tail_cons,
|
||||
head_fin_const, cons_val_one, head_cons, Fin.zero_eta, crossProduct, uRow, cRow,
|
||||
LinearMap.mk₂_apply, Pi.conj_apply, _root_.map_mul, map_inv₀, ← exp_conj, conj_I, conj_ofReal,
|
||||
|
|
@ -106,7 +108,7 @@ lemma sP_cross (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
|||
ring_nf
|
||||
rw [sin_sq]
|
||||
ring
|
||||
· simp only [tRow, sP, standardParameterizationAsMatrix, neg_mul, exp_neg, Fin.isValue, cons_val',
|
||||
· simp only [tRow, standParam, standParamAsMatrix, neg_mul, exp_neg, Fin.isValue, cons_val',
|
||||
cons_val_zero, empty_val', cons_val_fin_one, cons_val_two, tail_cons, head_fin_const,
|
||||
cons_val_one, head_cons, Fin.mk_one, crossProduct, uRow, cRow, LinearMap.mk₂_apply,
|
||||
Pi.conj_apply, _root_.map_mul, conj_ofReal, map_inv₀, ← exp_conj, conj_I, inv_inv, map_sub,
|
||||
|
|
@ -115,7 +117,7 @@ lemma sP_cross (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
|||
ring_nf
|
||||
rw [sin_sq]
|
||||
ring
|
||||
· simp only [tRow, sP, standardParameterizationAsMatrix, neg_mul, exp_neg, Fin.isValue,
|
||||
· simp only [tRow, standParam, standParamAsMatrix, neg_mul, exp_neg, Fin.isValue,
|
||||
cons_val', cons_val_zero, empty_val', cons_val_fin_one, cons_val_two, tail_cons, head_fin_const,
|
||||
cons_val_one, head_cons, Fin.reduceFinMk, crossProduct, uRow, cRow, LinearMap.mk₂_apply,
|
||||
Pi.conj_apply, _root_.map_mul, conj_ofReal, map_inv₀, ← exp_conj, conj_I, inv_inv, map_sub,
|
||||
|
|
@ -125,27 +127,26 @@ lemma sP_cross (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
|
|||
rw [sin_sq]
|
||||
ring
|
||||
|
||||
lemma eq_sP (U : CKMMatrix) {θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ} (hu : [U]u = [sP θ₁₂ θ₁₃ θ₂₃ δ₁₃]u)
|
||||
(hc : [U]c = [sP θ₁₂ θ₁₃ θ₂₃ δ₁₃]c) (hU : [U]t = conj [U]u ×₃ conj [U]c) :
|
||||
U = sP θ₁₂ θ₁₃ θ₂₃ δ₁₃ := by
|
||||
lemma eq_rows (U : CKMMatrix) {θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ} (hu : [U]u = [standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃]u)
|
||||
(hc : [U]c = [standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃]c) (hU : [U]t = conj [U]u ×₃ conj [U]c) :
|
||||
U = standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃ := by
|
||||
apply ext_Rows hu hc
|
||||
rw [hU, sP_cross, hu, hc]
|
||||
rw [hU, cross_product_t, hu, hc]
|
||||
|
||||
lemma eq_phases_sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ δ₁₃' : ℝ) (h : cexp (δ₁₃ * I) = cexp (δ₁₃' * I)) :
|
||||
sP θ₁₂ θ₁₃ θ₂₃ δ₁₃ = sP θ₁₂ θ₁₃ θ₂₃ δ₁₃' := by
|
||||
simp [sP, standardParameterizationAsMatrix]
|
||||
lemma eq_exp_of_phases (θ₁₂ θ₁₃ θ₂₃ δ₁₃ δ₁₃' : ℝ) (h : cexp (δ₁₃ * I) = cexp (δ₁₃' * I)) :
|
||||
standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃ = standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃' := by
|
||||
simp [standParam, standParamAsMatrix]
|
||||
apply CKMMatrix_ext
|
||||
simp
|
||||
rw [show exp (I * δ₁₃) = exp (I * δ₁₃') by rw [mul_comm, h, mul_comm]]
|
||||
rw [show cexp (-(I * ↑δ₁₃)) = cexp (-(I * ↑δ₁₃')) by rw [exp_neg, exp_neg, mul_comm, h, mul_comm]]
|
||||
|
||||
namespace Invariant
|
||||
|
||||
lemma VusVubVcdSq_sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Real.sin θ₁₂)
|
||||
open Invariant in
|
||||
lemma VusVubVcdSq_eq (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Real.sin θ₁₂)
|
||||
(h2 : 0 ≤ Real.cos θ₁₃) (h3 : 0 ≤ Real.sin θ₂₃) (h4 : 0 ≤ Real.cos θ₁₂) :
|
||||
VusVubVcdSq ⟦sP θ₁₂ θ₁₃ θ₂₃ δ₁₃⟧ =
|
||||
VusVubVcdSq ⟦standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃⟧ =
|
||||
Real.sin θ₁₂ ^ 2 * Real.cos θ₁₃ ^ 2 * Real.sin θ₁₃ ^ 2 * Real.sin θ₂₃ ^ 2 := by
|
||||
simp only [VusVubVcdSq, VusAbs, VAbs, VAbs', Fin.isValue, sP, standardParameterizationAsMatrix,
|
||||
simp only [VusVubVcdSq, VusAbs, VAbs, VAbs', Fin.isValue, standParam, standParamAsMatrix,
|
||||
neg_mul, Quotient.lift_mk, cons_val', cons_val_one, head_cons,
|
||||
empty_val', cons_val_fin_one, cons_val_zero, _root_.map_mul, VubAbs, cons_val_two, tail_cons,
|
||||
VcbAbs, VudAbs, Complex.abs_ofReal]
|
||||
|
|
@ -164,12 +165,13 @@ lemma VusVubVcdSq_sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Rea
|
|||
rw [hx]
|
||||
simp
|
||||
|
||||
lemma mulExpδ₃_sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Real.sin θ₁₂)
|
||||
open Invariant in
|
||||
lemma mulExpδ₁₃_eq (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Real.sin θ₁₂)
|
||||
(h2 : 0 ≤ Real.cos θ₁₃) (h3 : 0 ≤ Real.sin θ₂₃) (h4 : 0 ≤ Real.cos θ₁₂) :
|
||||
mulExpδ₃ ⟦sP θ₁₂ θ₁₃ θ₂₃ δ₁₃⟧ =
|
||||
mulExpδ₁₃ ⟦standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃⟧ =
|
||||
sin θ₁₂ * cos θ₁₃ ^ 2 * sin θ₂₃ * sin θ₁₃ * cos θ₁₂ * cos θ₂₃ * cexp (I * δ₁₃) := by
|
||||
rw [mulExpδ₃, VusVubVcdSq_sP _ _ _ _ h1 h2 h3 h4 ]
|
||||
simp only [jarlskogℂ, sP, standardParameterizationAsMatrix, neg_mul,
|
||||
rw [mulExpδ₁₃, VusVubVcdSq_eq _ _ _ _ h1 h2 h3 h4 ]
|
||||
simp only [jarlskogℂ, standParam, standParamAsMatrix, neg_mul,
|
||||
Quotient.lift_mk, jarlskogℂCKM, Fin.isValue, cons_val', cons_val_one, head_cons,
|
||||
empty_val', cons_val_fin_one, cons_val_zero, cons_val_two, tail_cons, _root_.map_mul, ←
|
||||
exp_conj, map_neg, conj_I, conj_ofReal, neg_neg, map_sub]
|
||||
|
|
@ -179,6 +181,7 @@ lemma mulExpδ₃_sP (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Rea
|
|||
have h1 : cexp (I * δ₁₃) ≠ 0 := exp_ne_zero _
|
||||
field_simp
|
||||
|
||||
end Invariant
|
||||
|
||||
|
||||
end standParam
|
||||
end
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue