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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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2
HepLean/AnomalyCancellation/PureU1/Basic.lean
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@ -124,7 +124,7 @@ lemma pureU1_last {n : ℕ} (S : (PureU1 n.succ).LinSols) :
rw [Fin.sum_univ_castSucc] at hS
linear_combination hS
/-- Two solutions to the Linear ACCs for `n.succ` areq equal if their first `n` charges are
/-- Two solutions to the Linear ACCs for `n.succ` are equal if their first `n` charges are
equal. -/
lemma pureU1_anomalyFree_ext {n : ℕ} {S T : (PureU1 n.succ).LinSols}
(h : ∀ (i : Fin n), S.val i.castSucc = T.val i.castSucc) : S = T := by

2
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
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@ -61,7 +61,7 @@ lemma speciesVal (S : linearParameters) :
| 3 => rfl
| 4 => rfl
/-- The map from the linear paramaters to elements of `(SMNoGrav 1).LinSols`. -/
/-- The map from the linear parameters to elements of `(SMNoGrav 1).LinSols`. -/
def asLinear (S : linearParameters) : (SMNoGrav 1).LinSols :=
chargeToLinear S.asCharges (by
simp only [accSU2, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero,

4
HepLean/BeyondTheStandardModel/TwoHDM/GaugeOrbits.lean
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@ -84,8 +84,8 @@ lemma prodMatrix_smooth (Φ1 Φ2 : HiggsField) :
simpa only [prodMatrix, Fin.zero_eta, Fin.isValue, of_apply, cons_val', cons_val_zero,
empty_val', cons_val_fin_one] using smooth_innerProd _ _
/-- The map `prodMatrix` is invariant under the simultanous action of `gaugeAction` on the two Higgs
fields. -/
/-- The map `prodMatrix` is invariant under the simultaneous action of `gaugeAction` on the two
Higgs fields. -/
informal_lemma prodMatrix_invariant where
deps := [``prodMatrix, ``gaugeAction]

2
HepLean/FlavorPhysics/CKMMatrix/Basic.lean
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@ -422,7 +422,7 @@ def Rcscb (V : CKMMatrix) : ℂ := [V]cs / [V]cb
/-- The ratio of the `cs` and `cb` elements of a CKM matrix. -/
scoped[CKMMatrix] notation (name := cs_cb_ratio) "[" V "]cs|cb" => Rcscb V
/-- Multiplicying the ratio of the `cs` by `cb` element of a CKM matrix by the `cb` element
/-- Multiplying the ratio of the `cs` by `cb` element of a CKM matrix by the `cb` element
returns the `cs` element, as long as the `cb` element is non-zero. -/
lemma Rcscb_mul_cb {V : CKMMatrix} (h : [V]cb ≠ 0) : [V]cs = Rcscb V * [V]cb := by
rw [Rcscb]

4
HepLean/FlavorPhysics/CKMMatrix/Invariants.lean
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@ -50,8 +50,8 @@ lemma jarlskogℂCKM_equiv (V U : CKMMatrix) (h : V ≈ U) :
def jarlskogℂ : Quotient CKMMatrixSetoid → ℂ :=
Quotient.lift jarlskogℂCKM jarlskogℂCKM_equiv
/-- An invariant for CKM mtrices corresponding to the square of the absolute values
of the `us`, `ub` and `cb` elements multipled together divided by `(VudAbs V ^ 2 + VusAbs V ^2)`.
/-- An invariant for CKM matrices corresponding to the square of the absolute values
of the `us`, `ub` and `cb` elements multiplied together divided by `(VudAbs V ^ 2 + VusAbs V ^2)`.
-/
def VusVubVcdSq (V : Quotient CKMMatrixSetoid) : ℝ :=
VusAbs V ^ 2 * VubAbs V ^ 2 * VcbAbs V ^2 / (VudAbs V ^ 2 + VusAbs V ^2)

2
HepLean/FlavorPhysics/CKMMatrix/Relations.lean
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@ -44,7 +44,7 @@ lemma fst_row_normalized_abs (V : CKMMatrix) : abs [V]ud ^ 2 + abs [V]us ^ 2 + a
lemma snd_row_normalized_abs (V : CKMMatrix) : abs [V]cd ^ 2 + abs [V]cs ^ 2 + abs [V]cb ^ 2 = 1 :=
VAbs_sum_sq_row_eq_one ⟦V⟧ 1
/-- The absolute value squared of the thid rwo of a CKM matrix is `1`, in terms of `abs`. -/
/-- The absolute value squared of the third rwo of a CKM matrix is `1`, in terms of `abs`. -/
lemma thd_row_normalized_abs (V : CKMMatrix) : abs [V]td ^ 2 + abs [V]ts ^ 2 + abs [V]tb ^ 2 = 1 :=
VAbs_sum_sq_row_eq_one ⟦V⟧ 2

4
HepLean/Lorentz/ComplexTensor/PauliMatrices/Basic.lean
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@ -79,7 +79,7 @@ lemma tensorNode_pauliContrDown : {pauliContrDown | μ α β}ᵀ.tensor =
-/
set_option maxRecDepth 5000 in
/-- A rearanging of `pauliCoDown` to place the pauli matrices on the right. -/
/-- A rearranging of `pauliCoDown` to place the pauli matrices on the right. -/
lemma pauliCoDown_eq_metric_mul_pauliCo :
{pauliCoDown | μ α' β' = εL' | α α' ⊗ εR' | β β' ⊗ pauliCo | μ α β}ᵀ := by
conv =>
@ -128,7 +128,7 @@ lemma pauliCoDown_eq_metric_mul_pauliCo :
decide
set_option maxRecDepth 5000 in
/-- A rearanging of `pauliContrDown` to place the pauli matrices on the right. -/
/-- A rearranging of `pauliContrDown` to place the pauli matrices on the right. -/
lemma pauliContrDown_eq_metric_mul_pauliContr :
{pauliContrDown | μ α' β' = εL' | α α' ⊗
εR' | β β' ⊗ pauliContr | μ α β}ᵀ := by

4
HepLean/Lorentz/ComplexVector/Unit.lean
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@ -38,7 +38,7 @@ lemma contrCoUnitVal_expand_tmul : contrCoUnitVal =
rfl
/-- The contra-co unit for complex lorentz vectors as a morphism
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo`, manifesting the invaraince under
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo`, manifesting the invariance under
the `SL(2, ℂ)` action. -/
def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
hom := ModuleCat.ofHom {
@ -88,7 +88,7 @@ lemma coContrUnitVal_expand_tmul : coContrUnitVal =
rfl
/-- The co-contra unit for complex lorentz vectors as a morphism
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr`, manifesting the invaraince under
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr`, manifesting the invariance under
the `SL(2, ℂ)` action. -/
def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
hom := ModuleCat.ofHom {

8
HepLean/Lorentz/Group/Orthochronous.lean
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@ -29,7 +29,7 @@ open Lorentz.Contr
/-- A Lorentz transformation is `orthochronous` if its `0 0` element is non-negative. -/
def IsOrthochronous : Prop := 0 ≤ Λ.1 (Sum.inl 0) (Sum.inl 0)
/-- A Lorentz transformation is `orthochronous` if and only if its fist column is
/-- A Lorentz transformation is `orthochronous` if and only if its first column is
future pointing. -/
lemma IsOrthochronous_iff_futurePointing :
IsOrthochronous Λ ↔ toNormOne Λ ∈ NormOne.FuturePointing d := by
@ -66,7 +66,7 @@ def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => Λ.1 (Sum.inl 0) (Sum.
/-- An auxiliary function used in the definition of `orthchroMapReal`.
This function takes all elements of `ℝ` less then `-1` to `-1`,
all elements of `R` geater then `1` to `1` and peserves all other elements. -/
all elements of `R` greater then `1` to `1` and preserves all other elements. -/
def stepFunction : ℝ → ℝ := fun t =>
if t ≤ -1 then -1 else
if 1 ≤ t then 1 else t
@ -152,7 +152,7 @@ lemma mul_othchron_of_not_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h :
exact NormOne.FuturePointing.metric_reflect_not_mem_not_mem h h'
/-- The product of an orthochronous Lorentz transformations with a
non-orthochronous Loentz transformation is not orthochronous. -/
non-orthochronous Lorentz transformation is not orthochronous. -/
lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h : IsOrthochronous Λ)
(h' : ¬ IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
rw [not_orthochronous_iff_le_zero, LorentzGroup.inl_inl_mul]
@ -161,7 +161,7 @@ lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h : I
exact NormOne.FuturePointing.metric_reflect_mem_not_mem h h'
/-- The product of a non-orthochronous Lorentz transformations with an
orthochronous Loentz transformation is not orthochronous. -/
orthochronous Lorentz transformation is not orthochronous. -/
lemma mul_not_othchron_of_not_othchron_othchron {Λ Λ' : LorentzGroup d} (h : ¬ IsOrthochronous Λ)
(h' : IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
rw [not_orthochronous_iff_le_zero, LorentzGroup.inl_inl_mul]

8
HepLean/Lorentz/MinkowskiMatrix.lean
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@ -29,7 +29,7 @@ variable {d : ℕ}
/-- Notation for `minkowskiMatrix`. -/
scoped[minkowskiMatrix] notation "η" => minkowskiMatrix
/-- The Minkowski matrix is self-inveting. -/
/-- The Minkowski matrix is self-inverting. -/
@[simp]
lemma sq : @minkowskiMatrix d * minkowskiMatrix = 1 := by
simp only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_mul_diagonal]
@ -55,8 +55,8 @@ lemma sq : @minkowskiMatrix d * minkowskiMatrix = 1 := by
lemma eq_transpose : minkowskiMatrixᵀ = @minkowskiMatrix d := by
simp only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_transpose]
/-- The deteminant of the Minkowski matrix is equal to `-1` to the power
of the number of spactial dimensions. -/
/-- The determinant of the Minkowski matrix is equal to `-1` to the power
of the number of spatial dimensions. -/
@[simp]
lemma det_eq_neg_one_pow_d : (@minkowskiMatrix d).det = (- 1) ^ d := by
simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
@ -68,7 +68,7 @@ lemma η_apply_mul_η_apply_diag (μ : Fin 1 ⊕ Fin d) : η μ μ * η μ μ =
| Sum.inl _ => simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
| Sum.inr _ => simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
/-- The Minkowski matix as a block matrix. -/
/-- The Minkowski matrix as a block matrix. -/
lemma as_block : @minkowskiMatrix d =
Matrix.fromBlocks (1 : Matrix (Fin 1) (Fin 1) ℝ) 0 0 (-1 : Matrix (Fin d) (Fin d) ℝ) := by
rw [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, ← fromBlocks_diagonal]

2
HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean
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@ -301,7 +301,7 @@ lemma σSAL_span : ⊤ ≤ Submodule.span ℝ (Set.range σSAL') := by
def σSAL : Basis (Fin 1 ⊕ Fin 3) ℝ (selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :=
Basis.mk σSAL_linearly_independent σSAL_span
/-- The decomposition of a self-adjint matrix into the Pauli matrices (where `σi` are negated). -/
/-- The decomposition of a self-adjoint matrix into the Pauli matrices (where `σi` are negated). -/
lemma σSAL_decomp (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
M = (1/2 * (Matrix.trace (σ0 * M.1)).re) • σSAL (Sum.inl 0)
+ (-1/2 * (Matrix.trace (σ1 * M.1)).re) • σSAL (Sum.inr 0)

2
HepLean/Lorentz/SL2C/SelfAdjoint.lean
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@ -175,7 +175,7 @@ lemma toSelfAdjointMap_det_one' {M : ℂ²ˣ²} (hM : M.IsUpperTriangular) (detM
_ = 1 := by rw [hE]; simp [detD_one, detA_one]
/-- This promotes `Lorentz.SL2C.toSelfAdjointMap M` and its definitional equivalence,
`Lorentz.SL2C.toSelfAdjointMap' M`, to a linear equivalence by recognising the linear inverse to be
`Lorentz.SL2C.toSelfAdjointMap' M`, to a linear equivalence by recognizing the linear inverse to be
`Lorentz.SL2C.toSelfAdjointMap M⁻¹`, i.e., `Lorentz.SL2C.toSelfAdjointMap' M⁻¹`. -/
noncomputable def toSelfAdjointEquiv (M : ℂ²ˣ²) [Invertible M] : ℍ₂ ≃ₗ[ℝ] ℍ₂ where
toLinearMap := toSelfAdjointMap' M

6
HepLean/Lorentz/Weyl/Contraction.lean
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@ -174,11 +174,11 @@ lemma altLeftContraction_basis (i j : Fin 2) :
exact Eq.propIntro (fun a => id (Eq.symm a)) fun a => id (Eq.symm a)
/--
The linear map from rightHandedWeyl ⊗ altRightHandedWeyl to ℂ given by
summing over components of rightHandedWeyl and altRightHandedWeyl in the
The linear map from `rightHandedWeyl ⊗ altRightHandedWeyl` to `ℂ` given by
summing over components of `rightHandedWeyl` and `altRightHandedWeyl` in the
standard basis (i.e. the dot product).
The contraction of a right-handed Weyl fermion with a left-handed Weyl fermion.
In index notation this is ψ^{dot a} φ_{dot a}.
In index notation this is `ψ^{dot a} φ_{dot a}`.
-/
def rightAltContraction : rightHanded ⊗ altRightHanded ⟶ 𝟙_ (Rep ℂ SL(2,ℂ)) where
hom := ModuleCat.ofHom <| TensorProduct.lift rightAltBi

2
HepLean/Meta/Remark/Properties.lean
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@ -13,7 +13,7 @@ namespace HepLean
open Lean
variable {m} [Monad m] [MonadEnv m] [MonadError m]
/-- All remarks in the enviroment. -/
/-- All remarks in the environment. -/
def allRemarkInfo : m (Array RemarkInfo) := do
let env ← getEnv
return remarkExtension.getState env

4
HepLean/PerturbationTheory/FeynmanDiagrams/Momentum.lean
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@ -44,7 +44,7 @@ We define the direct sum of the edge and vertex momentum spaces.
-/
/-- The type which assocaites to each half-edge a `1`-dimensional vector space.
/-- The type which associates to each half-edge a `1`-dimensional vector space.
Corresponding to that spanned by its momentum. -/
def HalfEdgeMomenta : Type := F.𝓱𝓔 → ℝ
@ -89,7 +89,7 @@ instance : AddCommGroup F.EdgeMomenta := Pi.addCommGroup
/-- The edge momenta form a module over `ℝ`. -/
instance : Module ℝ F.EdgeMomenta := Pi.module _ _ _
/-- The type which assocaites to each ege a `1`-dimensional vector space.
/-- The type which associates to each ege a `1`-dimensional vector space.
Corresponding to that spanned by its total inflowing momentum. -/
def VertexMomenta : Type := F.𝓥 → ℝ

4
HepLean/PerturbationTheory/FieldOpAlgebra/NormalOrder/Lemmas.lean
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@ -224,7 +224,7 @@ For a field specification `𝓕`, an element `φ` of `𝓕.CrAnFieldOp`, a list
`[φ, 𝓝(φ₀…φₙ)]ₛ = ∑ i, 𝓢(φ, φ₀…φᵢ₋₁) • [φ, φᵢ]ₛ * 𝓝(φ₀…φᵢ₋₁φᵢ₊₁…φₙ)`.
The proof of this result ultimetly goes as follows
The proof of this result ultimately goes as follows
- The definition of `normalOrder` is used to rewrite `𝓝(φ₀…φₙ)` as a scalar multiple of
a `ofCrAnList φsn` where `φsn` is the normal ordering of `φ₀…φₙ`.
- `superCommuteF_ofCrAnListF_ofCrAnListF_eq_sum` is used to rewrite the super commutator of `φ`
@ -348,7 +348,7 @@ For a field specification `𝓕`, a `φ` in `𝓕.FieldOp` and a list `φs` of `
the following relation holds in the algebra `𝓕.FieldOpAlgebra`,
`φ * 𝓝(φ₀φ₁…φₙ) = 𝓝(φφ₀φ₁…φₙ) + ∑ i, (𝓢(φ,φ₀φ₁…φᵢ₋₁) • [anPart φ, φᵢ]ₛ) * 𝓝(φ₀φ₁…φᵢ₋₁φᵢ₊₁…φₙ)`.
The proof of ultimetly goes as follows:
The proof of ultimately goes as follows:
- `ofFieldOp_eq_crPart_add_anPart` is used to split `φ` into its creation and annihilation parts.
- The fact that `crPart φ * 𝓝(φ₀φ₁…φₙ) = 𝓝(crPart φ * φ₀φ₁…φₙ)` is used.
- The fact that `anPart φ * 𝓝(φ₀φ₁…φₙ)` is

2
HepLean/PerturbationTheory/FieldOpAlgebra/TimeOrder.lean
View file

@ -434,7 +434,7 @@ lemma timeOrder_ofFieldOpList_singleton (φ : 𝓕.FieldOp) :
list of `𝓕.FieldOp`, `𝓣(φ₀…φₙ)`, is equal to
`𝓢(φᵢ,φ₀…φᵢ₋₁) • φᵢ * 𝓣(φ₀…φᵢ₋₁φᵢ₊₁φₙ)` where `φᵢ` is the maximal time field in `φ₀…φₙ`.
The proof of this result ultimitley relies on basic properties of ordering and signs. -/
The proof of this result ultimately relies on basic properties of ordering and signs. -/
lemma timeOrder_eq_maxTimeField_mul_finset (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) :
𝓣(ofFieldOpList (φ :: φs)) = 𝓢(𝓕 |>ₛ maxTimeField φ φs, 𝓕 |>ₛ ⟨(eraseMaxTimeField φ φs).get,
(Finset.univ.filter (fun x =>

2
HepLean/PerturbationTheory/FieldOpAlgebra/Universality.lean
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@ -75,7 +75,7 @@ lemma universalLift_ι {A : Type} [Semiring A] [Algebra ℂ A] (f : 𝓕.CrAnFie
universalLift f h1 (ι a) = FreeAlgebra.lift ℂ f a := by rfl
/--
For a field specification, `𝓕`, the algebra `𝓕.FieldOpAlgebra` satifies the following universal
For a field specification, `𝓕`, the algebra `𝓕.FieldOpAlgebra` satisfies the following universal
property. Let `f : 𝓕.CrAnFieldOp → A` be a function and `g : 𝓕.FieldOpFreeAlgebra →ₐ[ℂ] A`
the universal lift of that function associated with the free algebra `𝓕.FieldOpFreeAlgebra`.
If `g` is zero on the ideal defining `𝓕.FieldOpAlgebra`, then there is a unique

6
HepLean/PerturbationTheory/FieldOpFreeAlgebra/Basic.lean
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@ -55,7 +55,7 @@ def ofCrAnOpF (φ : 𝓕.CrAnFieldOp) : FieldOpFreeAlgebra 𝓕 :=
The algebra `𝓕.FieldOpFreeAlgebra` satisfies the universal property that for any other algebra
`A` (e.g. the operator algebra of the theory) with a map `f : 𝓕.CrAnFieldOp → A` (e.g.
the inclusion of the creation and annihilation parts of field operators into the
operator algebra) there is a unqiue algebra map `g : 𝓕.FieldOpFreeAlgebra → A`
operator algebra) there is a unique algebra map `g : 𝓕.FieldOpFreeAlgebra → A`
such that `g ∘ ofCrAnOpF = f`.
The unique `g` is given by `FreeAlgebra.lift ℂ f`.
@ -141,7 +141,7 @@ lemma ofFieldOpListF_sum (φs : List 𝓕.FieldOp) :
-/
/-- The algebra map taking an element of the free-state algbra to
/-- The algebra map taking an element of the free-state algebra to
the part of it in the creation and annihilation free algebra
spanned by creation operators. -/
def crPartF : 𝓕.FieldOp → 𝓕.FieldOpFreeAlgebra := fun φ =>
@ -166,7 +166,7 @@ lemma crPartF_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ))
crPartF (FieldOp.outAsymp φ) = 0 := by
simp [crPartF]
/-- The algebra map taking an element of the free-state algbra to
/-- The algebra map taking an element of the free-state algebra to
the part of it in the creation and annihilation free algebra
spanned by annihilation operators. -/
def anPartF : 𝓕.FieldOp → 𝓕.FieldOpFreeAlgebra := fun φ =>

4
HepLean/PerturbationTheory/FieldSpecification/CrAnFieldOp.lean
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@ -34,7 +34,7 @@ In this module in addition to defining `CrAnFieldOp` we also define some maps:
namespace FieldSpecification
variable (𝓕 : FieldSpecification)
/-- To each field operator the specificaition of the type of creation and annihilation parts.
/-- To each field operator the specification of the type of creation and annihilation parts.
For asymptotic states there is only one allowed part, whilst for position
field operator there is two. -/
def fieldOpToCrAnType : 𝓕.FieldOp → Type
@ -92,7 +92,7 @@ def crAnFieldOpToCreateAnnihilate : 𝓕.CrAnFieldOp → CreateAnnihilate
/-- For a field specification `𝓕`, and an element `φ` in `𝓕.CrAnFieldOp`, the field
statistic `crAnStatistics φ` is defined to be the statistic associated with the field `𝓕.Field`
(or equivalently `𝓕.FieldOp`) underlying `φ`.
(or `𝓕.FieldOp`) underlying `φ`.
The following notation is used in relation to `crAnStatistics`:
- For `φ` an element of `𝓕.CrAnFieldOp`, `𝓕 |>ₛ φ` is `crAnStatistics φ`.

2
HepLean/PerturbationTheory/FieldStatistics/Basic.lean
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@ -291,7 +291,7 @@ lemma ofList_take_insertIdx_le (n m : ℕ) (φ1 : 𝓕) (φs : List 𝓕) (hn :
· exact hn
· exact hm
/-- The instance of an addative monoid on `FieldStatistic`. -/
/-- The instance of an additive monoid on `FieldStatistic`. -/
instance : AddMonoid FieldStatistic where
zero := bosonic
add a b := a * b

2
HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean
View file

@ -34,7 +34,7 @@ open HepLean.Fin
of `φ` (at position `i`) with the new position of `j` after `φ` is added.
In other words, `φsΛ.insertAndContract φ i j` is formed by adding `φ` to `φs` at position `i`,
and contracting `φ` with the field orginally at position `j` if `j` is not none.
and contracting `φ` with the field originally at position `j` if `j` is not none.
The notation `φsΛ ↩Λ φ i j` is used to denote `φsΛ.insertAndContract φ i j`. -/
def insertAndContract {φs : List 𝓕.FieldOp} (φ : 𝓕.FieldOp) (φsΛ : WickContraction φs.length)

4
HepLean/PerturbationTheory/WickContraction/Sign/InsertSome.lean
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@ -201,7 +201,7 @@ lemma signFinset_insertAndContract_some (φ : 𝓕.FieldOp) (φs : List 𝓕.Fie
rw [Fin.succAbove_lt_succAbove_iff]
/--
Given a Wick contraction `φsΛ` the sign defined in the followin way,
Given a Wick contraction `φsΛ` the sign defined in the following way,
related to inserting a field `φ` at position `i` and contracting it with `j : φsΛ.uncontracted`.
- For each contracted pair `{a1, a2}` in `φsΛ` with `a1 < a2` the sign
`𝓢(φ, φₐ₂)` if `a₁ < i ≤ a₂` and `a₁ < j`.
@ -220,7 +220,7 @@ def signInsertSomeProd (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) (φsΛ : Wi
else
1
/-- Given a Wick contraction `φsΛ` the sign defined in the followin way,
/-- Given a Wick contraction `φsΛ` the sign defined in the following way,
related to inserting a field `φ` at position `i` and contracting it with `j : φsΛ.uncontracted`.
- If `j < i`, for each field `φₐ` in `φⱼ₊₁…φᵢ₋₁` without a dual at position `< j`
the sign `𝓢(φₐ, φᵢ)`.

2
HepLean/PerturbationTheory/WickContraction/SubContraction.lean
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@ -21,7 +21,7 @@ open HepLean.List
open FieldOpAlgebra
/-- Given a Wick contraction `φsΛ`, and a subset of `φsΛ.1`, the Wick contraction
conisting of contracted pairs within that subset. -/
consisting of contracted pairs within that subset. -/
def subContraction (S : Finset (Finset (Fin φs.length))) (ha : S ⊆ φsΛ.1) :
WickContraction φs.length :=
⟨S, by

2
HepLean/PerturbationTheory/WickContraction/TimeCond.lean
View file

@ -314,7 +314,7 @@ lemma empty_not_haveEqTime {φs : List 𝓕.FieldOp} :
rw [haveEqTime_iff_finset]
simp [empty]
/-- Given a Wick contraction the subset of contracted pairs between eqaul time fields. -/
/-- Given a Wick contraction the subset of contracted pairs between equal time fields. -/
def eqTimeContractSet {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length) :
Finset (Finset (Fin φs.length)) :=
Finset.univ.filter (fun a =>

4
HepLean/StandardModel/Basic.lean
View file

@ -52,7 +52,7 @@ See https://math.ucr.edu/home/baez/guts.pdf
informal_definition gaugeGroupℤ₂SubGroup where
deps := [``GaugeGroupI, ``StandardModel.gaugeGroupℤ₆SubGroup]
/-- The guage group of the Standard Model with a ℤ₂ quotient, i.e., the quotient of `GaugeGroupI` by
/-- The gauge group of the Standard Model with a ℤ₂ quotient, i.e., the quotient of `GaugeGroupI` by
the ℤ₂-subgroup `gaugeGroupℤ₂SubGroup`.
See https://math.ucr.edu/home/baez/guts.pdf
@ -69,7 +69,7 @@ See https://math.ucr.edu/home/baez/guts.pdf
informal_definition gaugeGroupℤ₃SubGroup where
deps := [``GaugeGroupI, ``StandardModel.gaugeGroupℤ₆SubGroup]
/-- The guage group of the Standard Model with a ℤ₃-quotient, i.e., the quotient of `GaugeGroupI` by
/-- The gauge group of the Standard Model with a ℤ₃-quotient, i.e., the quotient of `GaugeGroupI` by
the ℤ₃-subgroup `gaugeGroupℤ₃SubGroup`.
See https://math.ucr.edu/home/baez/guts.pdf

14
HepLean/StandardModel/HiggsBoson/GaugeAction.lean
View file

@ -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

4
HepLean/StandardModel/HiggsBoson/Potential.lean
View file

@ -120,7 +120,7 @@ lemma toFun_eq_zero_iff (h : P.𝓵 ≠ 0) (φ : HiggsField) (x : SpaceTime) :
-/
/-- The discrimiant of the quadratic equation formed by the Higgs potential. -/
/-- The discriminant of the quadratic equation formed by the Higgs potential. -/
def quadDiscrim (φ : HiggsField) (x : SpaceTime) : ℝ := discrim P.𝓵 (- P.μ2) (- P.toFun φ x)
/-- The discriminant of the quadratic formed by the potential is non-negative. -/
@ -325,7 +325,7 @@ lemma isBounded_of_𝓵_pos (h : 0 < P.𝓵) : P.IsBounded := by
/-- When there is no quartic coupling, the potential is bounded iff the mass squared is
non-positive, i.e., for `P : Potential` then `P.IsBounded` iff `P.μ2 ≤ 0`. That is to say
`- P.μ2 * ‖φ‖_H^2 x` is bounded below ifff `P.μ2 ≤ 0`. -/
`- P.μ2 * ‖φ‖_H^2 x` is bounded below iff `P.μ2 ≤ 0`. -/
informal_lemma isBounded_iff_of_𝓵_zero where
deps := [`StandardModel.HiggsField.Potential.IsBounded, `StandardModel.HiggsField.Potential]

2
HepLean/Tensors/OverColor/Iso.lean
View file

@ -90,7 +90,7 @@ lemma equivToIso_mkIso_inv {c1 c2 : X → C} (h : c1 = c2) :
Hom.toEquiv (mkIso h).inv = Equiv.refl _ := by
rfl
/-- The homorophism from `mk c` to `mk c1` obtaied by an equivalence and
/-- The morphism from `mk c` to `mk c1` obtained by an equivalence and
an equality lemma. -/
def equivToHomEq {c : X → C} {c1 : Y → C} (e : X ≃ Y)
(h : ∀ x, c1 x = (c ∘ e.symm) x := by decide) : mk c ⟶ mk c1 :=

6
HepLean/Tensors/TensorSpecies/Basic.lean
View file

@ -93,13 +93,13 @@ open OverColor
variable (S : TensorSpecies)
/-- The field `k` of a TensorSpecies has the instance of a commutative ring. -/
/-- The field `k` of a `TensorSpecies` has the instance of a commutative ring. -/
instance : CommRing S.k := S.k_commRing
/-- The field `G` of a TensorSpecies has the instance of a group. -/
/-- The field `G` of a `TensorSpecies` has the instance of a group. -/
instance : Group S.G := S.G_group
/-- The field `repDim` of a TensorSpecies is non-zero for all colors. -/
/-- The field `repDim` of a `TensorSpecies` is non-zero for all colors. -/
instance (c : S.C) : NeZero (S.repDim c) := S.repDim_neZero c
/-- The lift of the functor `S.F` to functor. -/

2
HepLean/Tensors/TensorSpecies/UnitTensor.lean
View file

@ -97,7 +97,7 @@ lemma unitTensor_eq_dual_perm (c : S.C) : {S.unitTensor c | μ ν}ᵀ.tensor =
exact congrFun (congrArg (fun f => f.toFun) hg) _
/-- The unit tensor of the dual of a color `c` is equal to the unit tensor of `c`
with indicees permuted. -/
with indices permuted. -/
lemma dual_unitTensor_eq_perm (c : S.C) :
{S.unitTensor (S.τ c) | ν μ}ᵀ.tensor = ({S.unitTensor c | μ ν}ᵀ |>
perm (OverColor.equivToHomEq (finMapToEquiv ![1, 0] ![1, 0])

2
HepLean/Tensors/Tree/NodeIdentities/Basic.lean
View file

@ -125,7 +125,7 @@ lemma perm_eq_id {n : ℕ} {c : Fin n → S.C} (σ : (OverColor.mk c) ⟶ (OverC
simp [perm_tensor, h]
/-- Given an equality of tensors corresponding to tensor trees where the tensor tree on the
left finishes with a premotion node, this permutation node can be moved to the
left finishes with a permutation node, this permutation node can be moved to the
tensor tree on the right. This lemma holds here for isomorphisms only, but holds in practice
more generally. -/
lemma perm_eq_of_eq_perm {n m : ℕ} {c : Fin n → S.C} {c1 : Fin m → S.C}

2
scripts/README.md
View file

@ -52,7 +52,7 @@ Uses openAI's API to check for spelling mistakes etc. in doc strings.
This code needs `https://github.com/jstoobysmith/Lean_llm_fork` to be installed.
It also needs the enviroment variable `OPENAI_API_KEY` defined using e.g.
It also needs the environment variable `OPENAI_API_KEY` defined using e.g.
```
export OPENAI_API_KEY=<Your-openAI-key>
```