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feat: Add real lorentz tensors

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jstoobysmith 2024-07-29 16:54:59 -04:00
parent 44b26efdaf
commit 99f4e85839
13 changed files with 602 additions and 48 deletions
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10
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -155,6 +155,16 @@ lemma coe_inv : (Λ⁻¹).1 = Λ.1⁻¹:= by
def transpose (Λ : LorentzGroup d) : LorentzGroup d :=
⟨Λ.1ᵀ, mem_iff_transpose.mp Λ.2⟩
@[simp]
lemma transpose_one : @transpose d 1 = 1 := by
apply Subtype.eq
exact Matrix.transpose_one
@[simp]
lemma transpose_mul : transpose (Λ * Λ') = transpose Λ' * transpose Λ := by
apply Subtype.eq
exact Matrix.transpose_mul Λ.1 Λ'.1
/-!
## Lorentz group as a topological group