feat: Refactor Index notation

HepLean/Tensors/ComplexLorentz/Basic.lean

@@ -0,0 +1,61 @@
+/-
+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.Tensors.OverColor.Basic
+import HepLean.Mathematics.PiTensorProduct
+/-!
+
+## Complex Lorentz tensors
+
+-/
+
+namespace Fermion
+
+open Matrix
+open MatrixGroups
+open Complex
+open TensorProduct
+open IndexNotation
+open CategoryTheory
+open MonoidalCategory
+
+/-- The colors associated with complex representations of SL(2, ℂ) of intrest to physics. -/
+inductive Color
+  | upL : Color
+  | downL : Color
+  | upR : Color
+  | downR : Color
+  | up : Color
+  | down : Color
+
+def τ : Color → Color
+  | Color.upL => Color.downL
+  | Color.downL => Color.upL
+  | Color.upR => Color.downR
+  | Color.downR => Color.upR
+  | Color.up => Color.down
+  | Color.down => Color.up
+
+def evalNo : Color → ℕ
+  | Color.upL => 2
+  | Color.downL => 2
+  | Color.upR => 2
+  | Color.downR => 2
+  | Color.up => 4
+  | Color.down => 4
+
+noncomputable section
+/-- The corresponding representations associated with a color. -/
+def colorToRep (c : Color) : Rep ℂ SL(2, ℂ) :=
+  match c with
+  | Color.upL => Fermion.altLeftHanded
+  | Color.downL => Fermion.leftHanded
+  | Color.upR => Fermion.altRightHanded
+  | Color.downR => Fermion.rightHanded
+  | Color.up => Lorentz.complexContr
+  | Color.down => Lorentz.complexCo
+
+end
+end Fermion