diff --git a/HepLean.lean b/HepLean.lean index a821102..ea534f2 100644 --- a/HepLean.lean +++ b/HepLean.lean @@ -103,6 +103,7 @@ import HepLean.Mathematics.Fin import HepLean.Mathematics.LinearMaps import HepLean.Mathematics.PiTensorProduct import HepLean.Mathematics.SO3.Basic +import HepLean.Mathematics.SuperAlgebra.Basic import HepLean.Meta.AllFilePaths import HepLean.Meta.Basic import HepLean.Meta.Informal diff --git a/HepLean/Mathematics/SuperAlgebra/Basic.lean b/HepLean/Mathematics/SuperAlgebra/Basic.lean new file mode 100644 index 0000000..9496d87 --- /dev/null +++ b/HepLean/Mathematics/SuperAlgebra/Basic.lean @@ -0,0 +1,23 @@ +/- +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 Mathlib.RingTheory.GradedAlgebra.Basic +import HepLean.Meta.Informal +/-! + +# Super Algebras + +A super algebra is a special type of graded algebra. + +It is used in physics to model the commutator of fermionic operators among themselves, +aswell as among bosonic operators. + +-/ + +informal_definition SuperAlgebra where + math :≈ "A super algebra is a graded algebra A with a ℤ₂ grading." + 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" diff --git a/HepLean/PerturbationTheory/Wick/Algebra.lean b/HepLean/PerturbationTheory/Wick/Algebra.lean index b5b0a1c..4d1fbe7 100644 --- a/HepLean/PerturbationTheory/Wick/Algebra.lean +++ b/HepLean/PerturbationTheory/Wick/Algebra.lean @@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Tooby-Smith -/ import HepLean.PerturbationTheory.Wick.Species +import HepLean.Mathematics.SuperAlgebra.Basic /-! # Operator algebra @@ -28,7 +29,7 @@ informal_definition WickAlgebra where math :≈ " Modifications of this may be needed. A structure with the following data: - - A ℤ₂-graded algebra A. + - A super algebra A. - A map from `ψ : 𝓔 × SpaceTime → A` where 𝓔 are field colors. - A map `ψc : 𝓔 × SpaceTime → A`. - A map `ψd : 𝓔 × SpaceTime → A`. @@ -47,6 +48,7 @@ informal_definition WickAlgebra where physics :≈ "This is defined to be an abstraction of the notion of an operator algebra." ref :≈ "https://physics.stackexchange.com/questions/24157/" + deps :≈ [``SuperAlgebra] informal_definition WickMonomial where math :≈ "The type of elements of the Wick algebra which is a product of fields." diff --git a/HepLean/PerturbationTheory/Wick/Species.lean b/HepLean/PerturbationTheory/Wick/Species.lean index 0fec956..d9d0733 100644 --- a/HepLean/PerturbationTheory/Wick/Species.lean +++ b/HepLean/PerturbationTheory/Wick/Species.lean @@ -22,8 +22,7 @@ namespace Wick /-- The basic structure needed to write down Wick contractions for a theory and calculate the corresponding Feynman diagrams. - WARNING: This definition is not yet complete. - -/ + WARNING: This definition is not yet complete. -/ structure Species where /-- The color of Field operators which appear in a theory. One may wish to call these `half-edges`, however we restrict this terminology