feat: Create Feynman diagram light
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HepLean/PerturbationTheory/FeynmanDiagrams/Light.lean
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HepLean/PerturbationTheory/FeynmanDiagrams/Light.lean
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.PerturbationTheory.Wick.Species
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/-!
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# Feynman diagrams
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This file currently contains a lighter implmentation of Feynman digrams than can be found in
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`HepLean.PerturbationTheory.FeynmanDiagrams.Basic`. Eventually this will superseed that file.
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The implmentation here is done in conjunction with Wicks species etc.
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This file is currently a stub.
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-/
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@ -11,8 +11,6 @@ import HepLean.PerturbationTheory.Wick.Species
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Currently this file is only for an example of Wick strings, correpsonding to a
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theory with two complex scalar fields. The concepts will however generalize.
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This file is currently a stub.
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We will formally define the operator ring, in terms of the fields present in the theory.
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## Futher reading
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@ -46,6 +44,8 @@ informal_definition WickAlgebra where
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Asympotic states:
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- `φc : 𝓔 × SpaceTime → A`. The creation asympotic state (incoming).
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- `φd : 𝓔 × SpaceTime → A`. The destruction asympotic state (outgoing).
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Subject to the conditions:
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...
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"
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physics :≈ "This is defined to be an
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abstraction of the notion of an operator algebra."
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@ -88,6 +88,17 @@ informal_definition normalOrder where
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end WickMonomial
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informal_definition asymptoicContract where
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math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator [φd(i), ψ(j)]."
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ref :≈ "See e.g. http://www.dylanjtemples.com:82/solutions/QFT_Solution_I-6.pdf"
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informal_definition contractAsymptotic where
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math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator [ψ(i), φc(j)]."
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informal_definition asymptoicContractAsymptotic where
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math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator
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[φd(i), φc(j)]."
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informal_definition contraction where
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math :≈ "Given two `i j : 𝓔 × SpaceTime`, the element of WickAlgebra
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defined by subtracting the normal ordering of `ψ i ψ j` from the time-ordering of
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