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feat: Make MulActionTensor

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jstoobysmith 2024-07-30 07:51:07 -04:00
parent 99f4e85839
commit a65fb06605
11 changed files with 177 additions and 55 deletions
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16
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -151,6 +151,22 @@ lemma coe_inv : (Λ⁻¹).1 = Λ.1⁻¹:= by
refine (inv_eq_left_inv ?h).symm
exact mem_iff_dual_mul_self.mp Λ.2
@[simp]
lemma subtype_inv_mul : (Subtype.val Λ)⁻¹ * (Subtype.val Λ) = 1 := by
trans Subtype.val (Λ⁻¹ * Λ)
rw [← coe_inv]
simp only [lorentzGroupIsGroup_inv, lorentzGroupIsGroup_mul_coe]
rw [inv_mul_self Λ]
simp only [lorentzGroupIsGroup_one_coe]
@[simp]
lemma subtype_mul_inv : (Subtype.val Λ) * (Subtype.val Λ)⁻¹ = 1 := by
trans Subtype.val (Λ * Λ⁻¹)
rw [← coe_inv]
simp only [lorentzGroupIsGroup_inv, lorentzGroupIsGroup_mul_coe]
rw [mul_inv_self Λ]
simp only [lorentzGroupIsGroup_one_coe]
/-- The transpose of a matrix in the Lorentz group is an element of the Lorentz group. -/
def transpose (Λ : LorentzGroup d) : LorentzGroup d :=
⟨Λ.1ᵀ, mem_iff_transpose.mp Λ.2⟩