feat: Add real lorentz tensors

HepLean/SpaceTime/LorentzVector/LorentzAction.lean

@@ -0,0 +1,30 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.SpaceTime.LorentzVector.Basic
+import HepLean.SpaceTime.LorentzGroup.Basic
+import Mathlib.RepresentationTheory.Basic
+/-!
+
+# Lorentz group action on Lorentz vectors.
+
+-/
+noncomputable section
+
+namespace LorentzVector
+
+variable {d : ℕ} (v : LorentzVector d)
+
+/-- The contravariant action of the Lorentz group on a Lorentz vector. -/
+def rep : Representation ℝ (LorentzGroup d) (LorentzVector d) where
+  toFun g := Matrix.toLinAlgEquiv e g
+  map_one' := by
+    simp only [lorentzGroupIsGroup_one_coe, map_one]
+  map_mul' x y := by
+    simp only [lorentzGroupIsGroup_mul_coe, map_mul]
+
+end LorentzVector
+
+end