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refactor: Some properties of field specifications (#285)

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* refactor: Fix field struct defn.

* rename: FieldStruct to FieldSpecification

* feat: Add examples of field specifications

* docs: Slight improvement of module docs
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Joseph Tooby-Smith 2025-01-21 06:11:47 +00:00 • committed by GitHub
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29 changed files with 153 additions and 126 deletions
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10
HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean
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@ -9,8 +9,8 @@ import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.Basic
# Super Commute
-/
namespace FieldStruct
variable {𝓕 : FieldStruct}
namespace FieldSpecification
variable {𝓕 : FieldSpecification}
namespace CrAnAlgebra
@ -18,7 +18,7 @@ open StateAlgebra
/-!
## The super commutor on the creation and annihlation algebra.
## The super commutor on the CrAnAlgebra.
-/
@ -35,7 +35,7 @@ noncomputable def superCommute : 𝓕.CrAnAlgebra →ₗ[ℂ] 𝓕.CrAnAlgebra
/-- The super commutor on the creation and annihlation algebra. For two bosonic operators
or a bosonic and fermionic operator this corresponds to the usual commutator
whilst for two fermionic operators this corresponds to the anti-commutator. -/
scoped[FieldStruct.CrAnAlgebra] notation "⟨" φs "," φs' "⟩ₛca" => superCommute φs φs'
scoped[FieldSpecification.CrAnAlgebra] notation "⟨" φs "," φs' "⟩ₛca" => superCommute φs φs'
lemma superCommute_ofCrAnList (φs φs' : List 𝓕.CrAnStates) : ⟨ofCrAnList φs, ofCrAnList φs'⟩ₛca =
ofCrAnList (φs ++ φs') - 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnList (φs' ++ φs) := by
@ -421,4 +421,4 @@ lemma superCommute_ofCrAnList_ofStateList_eq_sum (φs : List 𝓕.CrAnStates) :
end CrAnAlgebra
end FieldStruct
end FieldSpecification