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refactor: Move dual to minkowskiMatrix

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jstoobysmith 2024-11-08 11:16:16 +00:00
parent ac7c7939a7
commit 9fcaee7b2f
5 changed files with 60 additions and 54 deletions
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7
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -43,7 +43,7 @@ namespace LorentzGroup
scoped[LorentzGroup] notation (name := lorentzGroup_notation) "𝓛" => LorentzGroup
open minkowskiMetric
open minkowskiMatrix
variable {Λ Λ' : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ}
/-!
@ -123,7 +123,7 @@ instance lorentzGroupIsGroup : Group (LorentzGroup d) where
one := ⟨1, LorentzGroup.one_mem⟩
one_mul A := Subtype.eq (Matrix.one_mul A.1)
mul_one A := Subtype.eq (Matrix.mul_one A.1)
inv A := ⟨minkowskiMetric.dual A.1, LorentzGroup.dual_mem A.2⟩
inv A := ⟨minkowskiMatrix.dual A.1, LorentzGroup.dual_mem A.2⟩
inv_mul_cancel A := Subtype.eq (LorentzGroup.mem_iff_dual_mul_self.mp A.2)
/-- `LorentzGroup` has the subtype topology. -/
@ -132,6 +132,7 @@ instance : TopologicalSpace (LorentzGroup d) := instTopologicalSpaceSubtype
namespace LorentzGroup
open minkowskiMetric
open minkowskiMatrix
variable {Λ Λ' : LorentzGroup d}
@ -250,7 +251,7 @@ def toProd : LorentzGroup d →* (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ
(Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ)ᵐᵒᵖ :=
MonoidHom.comp (Units.embedProduct _) toGL
lemma toProd_eq_transpose_η : toProd Λ = (Λ.1, MulOpposite.op $ minkowskiMetric.dual Λ.1) := rfl
lemma toProd_eq_transpose_η : toProd Λ = (Λ.1, MulOpposite.op $ minkowskiMatrix.dual Λ.1) := rfl
lemma toProd_injective : Function.Injective (@toProd d) := by
intro A B h