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refactor: More spellings

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jstoobysmith 2025-02-10 10:59:09 +00:00
parent dc5b63c4a7
commit b4333f038a
10 changed files with 21 additions and 21 deletions
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4
HepLean/Lorentz/ComplexTensor/Metrics/Basis.lean
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@ -61,7 +61,7 @@ lemma coMetric_basis_expand_tree : {η' | μ ν}ᵀ.tensor =
(smul (-1) (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 3))))).tensor :=
coMetric_basis_expand
/-- The expansion of the Lorentz contrvariant metric in terms of basis vectors. -/
/-- The expansion of the Lorentz contravariant metric in terms of basis vectors. -/
lemma contrMatrix_basis_expand : {η | μ ν}ᵀ.tensor =
basisVector ![Color.up, Color.up] (fun _ => 0)
- basisVector ![Color.up, Color.up] (fun _ => 1)
@ -87,7 +87,7 @@ lemma contrMatrix_basis_expand : {η | μ ν}ᵀ.tensor =
simp only [Fin.isValue, Lorentz.complexContrBasisFin4, Basis.coe_reindex, Function.comp_apply]
rfl
/-- The expansion of the Lorentz contrvariant metric in terms of basis vectors as
/-- The expansion of the Lorentz contravariant metric in terms of basis vectors as
a structured tensor tree. -/
lemma contrMatrix_basis_expand_tree : {η | μ ν}ᵀ.tensor =
(TensorTree.add (tensorNode (basisVector ![Color.up, Color.up] (fun _ => 0))) <|

2
HepLean/Lorentz/MinkowskiMatrix.lean
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@ -118,7 +118,7 @@ def dual : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ := η * Λᵀ * η
lemma dual_id : @dual d 1 = 1 := by
simpa only [dual, transpose_one, mul_one] using minkowskiMatrix.sq
/-- The Minkowski dual swaps multiplications (acts contrvariantly). -/
/-- The Minkowski dual swaps multiplications (acts contravariantly). -/
@[simp]
lemma dual_mul : dual (Λ * Λ') = dual Λ' * dual Λ := by
simp only [dual, transpose_mul]

2
HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean
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@ -405,7 +405,7 @@ lemma σSAL_repr_inr_2 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
linear_combination (norm := ring_nf) -h0
simp only [σSAL, Basis.mk_repr, Fin.isValue, sub_self]
/-- The relationship between the basis `σSA` of contrvariant Pauli-matrices and the basis
/-- The relationship between the basis `σSA` of contravariant Pauli-matrices and the basis
`σSAL` of covariant Pauli matrices is by multiplication by the Minkowski matrix. -/
lemma σSA_minkowskiMetric_σSAL (i : Fin 1 ⊕ Fin 3) :
σSA i = minkowskiMatrix i i • σSAL i := by

2
HepLean/Lorentz/RealVector/Basic.lean
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@ -25,7 +25,7 @@ open minkowskiMatrix
Lorentz vectors. In index notation these have an up index `ψⁱ`. -/
def Contr (d : ℕ) : Rep ℝ (LorentzGroup d) := Rep.of ContrMod.rep
/-- The representation of contrvariant Lorentz vectors forms a topological space, induced
/-- The representation of contravariant Lorentz vectors forms a topological space, induced
by its equivalence to `Fin 1 ⊕ Fin d → ℝ`. -/
instance : TopologicalSpace (Contr d) := TopologicalSpace.induced
ContrMod.toFin1dℝEquiv (Pi.topologicalSpace)

2
HepLean/Lorentz/RealVector/Modules.lean
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@ -113,7 +113,7 @@ lemma stdBasis_apply (μ ν : Fin 1 ⊕ Fin d) : (stdBasis μ).val ν = if μ =
refine ite_congr ?h₁ (congrFun rfl) (congrFun rfl)
exact Eq.propIntro (fun a => id (Eq.symm a)) fun a => id (Eq.symm a)
/-- Decomposition of a contrvariant Lorentz vector into the standard basis. -/
/-- Decomposition of a contravariant Lorentz vector into the standard basis. -/
lemma stdBasis_decomp (v : ContrMod d) : v = ∑ i, v.toFin1dℝ i • stdBasis i := by
apply toFin1dℝEquiv.injective
simp only [map_sum, _root_.map_smul]