feat: Informal superCommuator

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jstoobysmith 2024-12-03 15:26:06 +00:00
parent b57e042f1a
commit fbc3abd83e
2 changed files with 10 additions and 1 deletions

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@ -21,3 +21,11 @@ informal_definition SuperAlgebra where
physics :≈ "A super algebra is used to model the commutator of fermionic operators among
themselves, aswell as among bosonic operators."
ref :≈ "https://en.wikipedia.org/wiki/Superalgebra"
namespace SuperAlgebra
informal_definition superCommuator where
math :≈ "The commutator which for `a ∈ Aᵢ` and `b ∈ Aⱼ` is defined as `ab - (-1)^(i * j) ba`."
deps :≈ [``SuperAlgebra]
end SuperAlgebra

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@ -27,7 +27,8 @@ inductive WickContract : {ni : } → {i : Fin ni → S.𝓯} → {n : }
(str : WickString i c o final) →
{k : } → (b1 : Fin k → Fin n) → (b2 : Fin k → Fin n) → Type where
| string {ni : } {i : Fin ni → S.𝓯} {n : } {c : Fin n → S.𝓯}
{no : } {o : Fin no → S.𝓯} {str : WickString i c o final} : WickContract str Fin.elim0 Fin.elim0
{no : } {o : Fin no → S.𝓯}
{str : WickString i c o final} : WickContract str Fin.elim0 Fin.elim0
| contr {ni : } {i : Fin ni → S.𝓯} {n : } {c : Fin n → S.𝓯}
{no : } {o : Fin no → S.𝓯} {str : WickString i c o final} {k : }
{b1 : Fin k → Fin n} {b2 : Fin k → Fin n} : (i : Fin n) →