47 lines
1.3 KiB
Text
47 lines
1.3 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.Tensors.Tree.Elab
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import HepLean.Tensors.ComplexLorentz.Basic
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import Mathlib.LinearAlgebra.TensorProduct.Basis
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import HepLean.Tensors.Tree.NodeIdentities.Basic
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import HepLean.Tensors.Tree.NodeIdentities.PermProd
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import HepLean.Tensors.Tree.NodeIdentities.PermContr
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import HepLean.Tensors.Tree.NodeIdentities.ProdComm
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import HepLean.Tensors.Tree.NodeIdentities.ContrSwap
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import HepLean.Tensors.Tree.NodeIdentities.ContrContr
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/-!
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## Bispinors
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-/
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open IndexNotation
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open CategoryTheory
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open MonoidalCategory
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open Matrix
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open MatrixGroups
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open Complex
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open TensorProduct
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open IndexNotation
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open CategoryTheory
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open TensorTree
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open OverColor.Discrete
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open Fermion
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noncomputable section
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namespace Lorentz
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namespace complexContr
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/-- A bispinor `pᵃᵃ` created from a lorentz vector `p^μ`. -/
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def bispinorUp (p : complexContr) :=
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{p | μ ⊗ (Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | ν α β)}ᵀ.tensor
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/-- A bispinor `pₐₐ` created from a lorentz vector `p^μ`. -/
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def bispinorDown (p : complexContr) :=
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{Fermion.altRightMetric | β β' ⊗ Fermion.altLeftMetric | α α' ⊗
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(complexContr.bispinorUp p) | α β}ᵀ.tensor
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end complexContr
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end Lorentz
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end
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