refactor: Note
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5 changed files with 27 additions and 19 deletions
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@ -125,28 +125,18 @@ def perturbationTheory : Note where
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as it appears in HepLean. We start with some basic definitions.",
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.h1 "Field operators",
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.h2 "Field statistics",
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.p "A quantum field can either be a bosonic or fermionic. This information is
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contained in the inductive type `FieldStatistic`. This is defined as follows:",
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.name `FieldStatistic,
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.p "Field statistics form a commuative group isomorphic to ℤ₂, with
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the bosonic element of `FieldStatistic` being the identity element.",
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.p "Most of our use of field statistics will come by comparing two field statistics
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and picking up a minus sign when they are both fermionic. This concept is
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made precise using the notion of an exchange sign, defined as:",
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.name `FieldStatistic.instCommGroup,
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.name `FieldStatistic.exchangeSign,
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.p "We use the notation `𝓢(a,b)` as shorthand for the exchange sign of `a` and `b`.",
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.h2 "Field specifications",
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.name `fieldSpecification_intro,
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.name `FieldSpecification,
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.p "Some examples of `FieldSpecification`s are given below:",
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.name `FieldSpecification.singleBoson,
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.name `FieldSpecification.singleFermion,
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.name `FieldSpecification.doubleBosonDoubleFermion,
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.h2 "Field operators",
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.name `FieldSpecification.FieldOp,
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.name `FieldSpecification.CrAnFieldOp,
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.h2 "Field-operator free algebra",
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.name `FieldSpecification.FieldOpFreeAlgebra,
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.name `FieldSpecification.FieldOpFreeAlgebra.naming_convention,
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.name `FieldSpecification.FieldOpFreeAlgebra.superCommuteF,
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.h2 "Field-operator algebra",
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.name `FieldSpecification.FieldOpAlgebra,
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