feat: Add defn of bispinors

HepLean/Tensors/ComplexLorentz/Bispinors/Basic.lean

@@ -0,0 +1,47 @@
+/-
+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.Tree.Elab
+import HepLean.Tensors.ComplexLorentz.Basic
+import Mathlib.LinearAlgebra.TensorProduct.Basis
+import HepLean.Tensors.Tree.NodeIdentities.Basic
+import HepLean.Tensors.Tree.NodeIdentities.PermProd
+import HepLean.Tensors.Tree.NodeIdentities.PermContr
+import HepLean.Tensors.Tree.NodeIdentities.ProdComm
+import HepLean.Tensors.Tree.NodeIdentities.ContrSwap
+import HepLean.Tensors.Tree.NodeIdentities.ContrContr
+/-!
+
+## Bispinors
+
+-/
+open IndexNotation
+open CategoryTheory
+open MonoidalCategory
+open Matrix
+open MatrixGroups
+open Complex
+open TensorProduct
+open IndexNotation
+open CategoryTheory
+open TensorTree
+open OverColor.Discrete
+open Fermion
+noncomputable section
+namespace Lorentz
+namespace complexContr
+
+/-- A bispinor `pᵃᵃ` created from a lorentz vector  `p^μ`. -/
+def bispinorUp (p : complexContr) :=
+  {p | μ ⊗ (Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | ν α β)}ᵀ.tensor
+
+/-- A bispinor `pₐₐ` created from a lorentz vector  `p^μ`. -/
+def bispinorDown (p : complexContr) :=
+  {Fermion.altRightMetric | β β' ⊗ Fermion.altLeftMetric | α α' ⊗
+    (complexContr.bispinorUp p) | α β}ᵀ.tensor
+
+end complexContr
+end Lorentz
+end