DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: Lint

Browse source
This commit is contained in:
jstoobysmith 2024-11-11 07:22:36 +00:00
parent a8243f4e79
commit 081955c993
6 changed files with 35 additions and 34 deletions
Download patch file Download diff file Expand all files Collapse all files

37
HepLean/Lorentz/SL2C/Basic.lean
View file

@ -83,7 +83,7 @@ lemma toSelfAdjointMap_apply_σSAL_inl (M : SL(2, ℂ)) :
(- ((M.1 0 1).re * (M.1 1 1).re + (M.1 0 1).im * (M.1 1 1).im +
(M.1 0 0).im * (M.1 1 0).im + (M.1 0 0).re * (M.1 1 0).re)) • PauliMatrix.σSAL (Sum.inr 0)
+ ((- (M.1 0 0).re * (M.1 1 0).im + ↑(M.1 1 0).re * (M.1 0 0).im
- (M.1 0 1).re * (M.1 1 1).im + (M.1 0 1).im * (M.1 1 1).re)) • PauliMatrix.σSAL (Sum.inr 1)
- (M.1 0 1).re * (M.1 1 1).im + (M.1 0 1).im * (M.1 1 1).re)) • PauliMatrix.σSAL (Sum.inr 1)
+ ((- ‖M.1 0 0‖ ^ 2 - ‖M.1 0 1‖ ^ 2 + ‖M.1 1 0‖ ^ 2 + ‖M.1 1 1‖ ^ 2) / 2) •
PauliMatrix.σSAL (Sum.inr 2) := by
simp only [toSelfAdjointMap, PauliMatrix.σSAL, Fin.isValue, Basis.coe_mk, PauliMatrix.σSAL',
@ -97,34 +97,43 @@ lemma toSelfAdjointMap_apply_σSAL_inl (M : SL(2, ℂ)) :
conv => lhs; erw [← eta_fin_two 1, mul_one]
conv => lhs; lhs; rw [eta_fin_two M.1]
conv => lhs; rhs; rw [eta_fin_two M.1ᴴ]
simp
simp only [Fin.isValue, conjTranspose_apply, RCLike.star_def, cons_mul, Nat.succ_eq_add_one,
Nat.reduceAdd, vecMul_cons, head_cons, smul_cons, smul_eq_mul, smul_empty, tail_cons,
empty_vecMul, add_zero, add_cons, empty_add_empty, empty_mul, Equiv.symm_apply_apply,
EmbeddingLike.apply_eq_iff_eq]
rw [mul_conj', mul_conj', mul_conj', mul_conj']
ext x y
match x, y with
| 0, 0 =>
simp
simp only [Fin.isValue, norm_eq_abs, cons_val', cons_val_zero, empty_val', cons_val_fin_one]
ring_nf
| 0, 1 =>
simp
simp only [Fin.isValue, norm_eq_abs, cons_val', cons_val_one, head_cons, empty_val',
cons_val_fin_one, cons_val_zero]
ring_nf
rw [← re_add_im (M.1 0 0), ← re_add_im (M.1 0 1), ← re_add_im (M.1 1 0), ← re_add_im (M.1 1 1)]
simp [- re_add_im]
simp only [Fin.isValue, map_add, conj_ofReal, _root_.map_mul, conj_I, mul_neg, add_re,
ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self, add_zero, add_im,
mul_im, zero_add]
ring_nf
simp
simp only [Fin.isValue, I_sq, mul_neg, mul_one, neg_mul, neg_neg, one_mul, sub_neg_eq_add]
ring
| 1, 0 =>
simp
simp only [Fin.isValue, norm_eq_abs, cons_val', cons_val_zero, empty_val', cons_val_fin_one,
cons_val_one, head_fin_const]
ring_nf
rw [← re_add_im (M.1 0 0), ← re_add_im (M.1 0 1), ← re_add_im (M.1 1 0), ← re_add_im (M.1 1 1)]
simp [- re_add_im]
simp only [Fin.isValue, map_add, conj_ofReal, _root_.map_mul, conj_I, mul_neg, add_re,
ofReal_re, mul_re, I_re, mul_zero, ofReal_im, I_im, mul_one, sub_self, add_zero, add_im,
mul_im, zero_add]
ring_nf
simp
simp only [Fin.isValue, I_sq, mul_neg, mul_one, neg_mul, neg_neg, one_mul, sub_neg_eq_add]
ring
| 1, 1 =>
simp
simp only [Fin.isValue, norm_eq_abs, cons_val', cons_val_one, head_cons, empty_val',
cons_val_fin_one, head_fin_const]
ring_nf
/-- The monoid homomorphisms from `SL(2, ℂ)` to matrices indexed by `Fin 1 ⊕ Fin 3`
formed by the action `M A Mᴴ`. -/
def toMatrix : SL(2, ℂ) →* Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ where
@ -216,15 +225,15 @@ lemma toLorentzGroup_fst_col (M : SL(2, ℂ)) :
(fun μ => (toLorentzGroup M).1 μ (Sum.inl 0)) = fun μ =>
match μ with
| Sum.inl 0 => ((‖M.1 0 0‖ ^ 2 + ‖M.1 0 1‖ ^ 2 + ‖M.1 1 0‖ ^ 2 + ‖M.1 1 1‖ ^ 2) / 2)
| Sum.inr 0 => (- ((M.1 0 1).re * (M.1 1 1).re + (M.1 0 1).im * (M.1 1 1).im +
| Sum.inr 0 => (- ((M.1 0 1).re * (M.1 1 1).re + (M.1 0 1).im * (M.1 1 1).im +
(M.1 0 0).im * (M.1 1 0).im + (M.1 0 0).re * (M.1 1 0).re))
| Sum.inr 1 => ((- (M.1 0 0).re * (M.1 1 0).im + ↑(M.1 1 0).re * (M.1 0 0).im
- (M.1 0 1).re * (M.1 1 1).im + (M.1 0 1).im * (M.1 1 1).re))
| Sum.inr 2 => ((- ‖M.1 0 0‖ ^ 2 - ‖M.1 0 1‖ ^ 2 + ‖M.1 1 0‖ ^ 2 + ‖M.1 1 1‖ ^ 2) / 2) := by
let k : Fin 1 ⊕ Fin 3 → ℝ := fun μ =>
let k : Fin 1 ⊕ Fin 3 → ℝ := fun μ =>
match μ with
| Sum.inl 0 => ((‖M.1 0 0‖ ^ 2 + ‖M.1 0 1‖ ^ 2 + ‖M.1 1 0‖ ^ 2 + ‖M.1 1 1‖ ^ 2) / 2)
| Sum.inr 0 => (- ((M.1 0 1).re * (M.1 1 1).re + (M.1 0 1).im * (M.1 1 1).im +
| Sum.inr 0 => (- ((M.1 0 1).re * (M.1 1 1).re + (M.1 0 1).im * (M.1 1 1).im +
(M.1 0 0).im * (M.1 1 0).im + (M.1 0 0).re * (M.1 1 0).re))
| Sum.inr 1 => ((- (M.1 0 0).re * (M.1 1 0).im + ↑(M.1 1 0).re * (M.1 0 0).im
- (M.1 0 1).re * (M.1 1 1).im + (M.1 0 1).im * (M.1 1 1).re))