feat: Add properties of Weyl fermions

2024-10-03 07:15:48 +00:00 · 2024-10-03 07:15:48 +00:00 · 24a20aef81
commit 24a20aef81
parent 0f1ca912cc
5 changed files with 743 additions and 55 deletions
--- a/HepLean/SpaceTime/SL2C/Basic.lean
+++ b/HepLean/SpaceTime/SL2C/Basic.lean
@ -26,6 +26,23 @@ open SpaceTime

 noncomputable section

+
+/-!
+
+## Some basic properties about SL(2, ℂ)
+
+Possibly to be moved to mathlib at some point.
+-/
+
+lemma inverse_coe (M : SL(2, ℂ)) : M.1⁻¹ = (M⁻¹).1 := by
+  apply Matrix.inv_inj
+  simp
+  have h1 : IsUnit M.1.det := by
+    simp
+  rw [Matrix.inv_adjugate M.1 h1]
+  · simp
+  · simp
+
 /-!

 ## Representation of SL(2, ℂ) on spacetime