38 lines
930 B
Text
38 lines
930 B
Text
/-
|
||
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.ComplexLorentz.PauliLower
|
||
/-!
|
||
|
||
## 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 complexLorentzTensor
|
||
open Lorentz
|
||
|
||
/-- A bispinor `pᵃᵃ` created from a lorentz vector `p^μ`. -/
|
||
def contrBispinorUp (p : complexContr) :=
|
||
{p | μ ⊗ pauliCo | μ 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 complexLorentzTensor
|
||
end
|