refactor: Note

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jstoobysmith 2025-02-04 15:53:27 +00:00
parent ff6c8955b5
commit 256a1c3e94
5 changed files with 27 additions and 19 deletions

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@ -125,28 +125,18 @@ def perturbationTheory : Note where
as it appears in HepLean. We start with some basic definitions.",
.h1 "Field operators",
.h2 "Field statistics",
.p "A quantum field can either be a bosonic or fermionic. This information is
contained in the inductive type `FieldStatistic`. This is defined as follows:",
.name `FieldStatistic,
.p "Field statistics form a commuative group isomorphic to ℤ₂, with
the bosonic element of `FieldStatistic` being the identity element.",
.p "Most of our use of field statistics will come by comparing two field statistics
and picking up a minus sign when they are both fermionic. This concept is
made precise using the notion of an exchange sign, defined as:",
.name `FieldStatistic.instCommGroup,
.name `FieldStatistic.exchangeSign,
.p "We use the notation `𝓢(a,b)` as shorthand for the exchange sign of `a` and `b`.",
.h2 "Field specifications",
.name `fieldSpecification_intro,
.name `FieldSpecification,
.p "Some examples of `FieldSpecification`s are given below:",
.name `FieldSpecification.singleBoson,
.name `FieldSpecification.singleFermion,
.name `FieldSpecification.doubleBosonDoubleFermion,
.h2 "Field operators",
.name `FieldSpecification.FieldOp,
.name `FieldSpecification.CrAnFieldOp,
.h2 "Field-operator free algebra",
.name `FieldSpecification.FieldOpFreeAlgebra,
.name `FieldSpecification.FieldOpFreeAlgebra.naming_convention,
.name `FieldSpecification.FieldOpFreeAlgebra.superCommuteF,
.h2 "Field-operator algebra",
.name `FieldSpecification.FieldOpAlgebra,