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refactor: Docs for FieldOpFreeAlgebra

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jstoobysmith 2025-02-06 10:47:34 +00:00
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9
HepLean/PerturbationTheory/FieldOpAlgebra/Basic.lean
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@ -42,9 +42,12 @@ def fieldOpIdealSet : Set (FieldOpFreeAlgebra 𝓕) :=
annihilation operators always super-commute.
- `[ofCrAnOpF φ, ofCrAnOpF φ']ₛca` for `φ` and `φ'` field operators with different statistics.
I.e. Fermions super-commute with bosons.
The algebra `𝓕.FieldOpAlgebra` is the most general (in the correct sense) algebra
satisfying these properties.
-/
The algebra `𝓕.FieldOpAlgebra` satisfies the following universal property. For any
algebra `A` (e.g. the operator algebra of the theory) with a map `f : 𝓕.CrAnFieldOp → A` (e.g.
the inclusion of the creation and annihilation parts of field operators into the operator algebra)
such that the image of `f` obey the relations above, there exists a unique algebra map
`g : 𝓕.FieldOpAlgebra → A` through which `f` factors. -/
abbrev FieldOpAlgebra : Type := (TwoSidedIdeal.span 𝓕.fieldOpIdealSet).ringCon.Quotient
namespace FieldOpAlgebra