feat: Add properties of Lorentz group

HepLean/StandardModel/CliffordAlgebra.lean

@@ -13,7 +13,7 @@ This file defines the Gamma matrices.
 
 - Prove that the algebra generated by the gamma matrices is ismorphic to the
   Clifford algebra assocaited with spacetime.
--
+- Include relations for gamma matrices.
 -/
 
 namespace StandardModel
@@ -41,22 +41,9 @@ def γ : Fin 4 → Matrix (Fin 4) (Fin 4) ℂ := ![γ0, γ1, γ2, γ3]
 
 namespace γ
 
-variable (μ : Fin 4)
-
-
-
-
-/-- The trace of the gamma matrices is zero. -/
-lemma trace_eq_zero (μ : Fin 4) : Matrix.trace (γ μ) = 0 := by
-  fin_cases μ
-    <;> simp [γ, γ0, γ1, γ2, γ3]
-    <;> rw [Matrix.trace, Fin.sum_univ_four]
-    <;> simp
-  any_goals rfl
-  change 0 + 0 = 0
-  simp [add_zero]
-
+open spaceTime
 
+variable (μ ν : Fin 4)
 
 @[simp]
 def γSet : Set (Matrix (Fin 4) (Fin 4) ℂ) := {γ i | i : Fin 4}