f8f94979ab
* make informal_definition and informal_lemma commands * drop the fields "math", "physics", and "proof" from InformalDefinition/InformalLemma and use docstrings instead * render informal docstring in dependency graph
62 lines
1.8 KiB
Text
62 lines
1.8 KiB
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.Lorentz.ComplexTensor.Metrics.Basis
|
||
import HepLean.Lorentz.ComplexTensor.Units.Basic
|
||
/-!
|
||
|
||
## Symmetry lemmas relating to units
|
||
|
||
-/
|
||
open IndexNotation
|
||
open CategoryTheory
|
||
open MonoidalCategory
|
||
open Matrix
|
||
open MatrixGroups
|
||
open Complex
|
||
open TensorProduct
|
||
open IndexNotation
|
||
open CategoryTheory
|
||
open TensorTree
|
||
open OverColor.Discrete
|
||
noncomputable section
|
||
|
||
namespace complexLorentzTensor
|
||
|
||
/-!
|
||
|
||
## Symmetry properties
|
||
|
||
-/
|
||
|
||
/-- Swapping indices of `coContrUnit` returns `contrCoUnit`: `{δ' | μ ν = δ | ν μ}ᵀ`. -/
|
||
informal_lemma coContrUnit_symm where
|
||
deps := [``coContrUnit, ``contrCoUnit]
|
||
|
||
/-- Swapping indices of `contrCoUnit` returns `coContrUnit`: `{δ | μ ν = δ' | ν μ}ᵀ`. -/
|
||
informal_lemma contrCoUnit_symm where
|
||
deps := [``contrCoUnit, ``coContrUnit]
|
||
|
||
/-- Swapping indices of `altLeftLeftUnit` returns `leftAltLeftUnit`: `{δL' | α α' = δL | α' α}ᵀ`. -/
|
||
informal_lemma altLeftLeftUnit_symm where
|
||
deps := [``altLeftLeftUnit, ``leftAltLeftUnit]
|
||
|
||
/-- Swapping indices of `leftAltLeftUnit` returns `altLeftLeftUnit`: `{δL | α α' = δL' | α' α}ᵀ`. -/
|
||
informal_lemma leftAltLeftUnit_symm where
|
||
deps := [``leftAltLeftUnit, ``altLeftLeftUnit]
|
||
|
||
/-- Swapping indices of `altRightRightUnit` returns `rightAltRightUnit`:
|
||
`{δR' | β β' = δR | β' β}ᵀ`.
|
||
-/
|
||
informal_lemma altRightRightUnit_symm where
|
||
deps := [``altRightRightUnit, ``rightAltRightUnit]
|
||
|
||
/-- Swapping indices of `rightAltRightUnit` returns `altRightRightUnit`:
|
||
`{δR | β β' = δR' | β' β}ᵀ`.
|
||
-/
|
||
informal_lemma rightAltRightUnit_symm where
|
||
deps := [``rightAltRightUnit, ``altRightRightUnit]
|
||
|
||
end complexLorentzTensor
|