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reactor: Removal of double spaces

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jstoobysmith 2024-07-12 11:23:02 -04:00
parent ce92e1d649
commit 13f62a50eb
64 changed files with 550 additions and 546 deletions
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10
HepLean/AnomalyCancellation/PureU1/Basic.lean
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@ -16,7 +16,7 @@ We define the anomaly cancellation conditions for a pure U(1) gauge theory with
universe v u
open Nat
open Finset
open Finset
namespace PureU1
open BigOperators
@ -37,7 +37,7 @@ def accGrav (n : ℕ) : ((PureU1Charges n).Charges →ₗ[ℚ] ℚ) where
/-- The symmetric trilinear form used to define the cubic anomaly. -/
@[simps!]
def accCubeTriLinSymm {n : ℕ} : TriLinearSymm (PureU1Charges n).Charges := TriLinearSymm.mk₃
(fun S => ∑ i, S.1 i * S.2.1 i * S.2.2 i)
(fun S => ∑ i, S.1 i * S.2.1 i * S.2.2 i)
(by
intro a S L T
simp [HSMul.hSMul]
@ -70,13 +70,13 @@ def accCubeTriLinSymm {n : ℕ} : TriLinearSymm (PureU1Charges n).Charges := Tri
/-- The cubic anomaly equation. -/
@[simp]
def accCube (n : ℕ) : HomogeneousCubic ((PureU1Charges n).Charges) :=
def accCube (n : ℕ) : HomogeneousCubic ((PureU1Charges n).Charges) :=
(accCubeTriLinSymm).toCubic
lemma accCube_explicit (n : ℕ) (S : (PureU1Charges n).Charges) :
accCube n S = ∑ i : Fin n, S i ^ 3:= by
rw [accCube, TriLinearSymm.toCubic]
change accCubeTriLinSymm S S S = _
change accCubeTriLinSymm S S S = _
rw [accCubeTriLinSymm]
simp only [PureU1Charges_numberCharges, TriLinearSymm.mk₃_toFun_apply_apply]
apply Finset.sum_congr
@ -99,7 +99,7 @@ def PureU1 (n : ℕ) : ACCSystem where
/-- An equivalence of vector spaces of charges when the number of fermions is equal. -/
def pureU1EqCharges {n m : ℕ} (h : n = m):
(PureU1 n).Charges ≃ₗ[ℚ] (PureU1 m).Charges where
(PureU1 n).Charges ≃ₗ[ℚ] (PureU1 m).Charges where
toFun f := f ∘ Fin.cast h.symm
invFun f := f ∘ Fin.cast h
map_add' _ _ := rfl