feat: Create Feynman diagram light

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jstoobysmith 2024-12-03 07:51:10 +00:00
parent 4e097b12f8
commit bc1321067d
3 changed files with 31 additions and 2 deletions

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@ -0,0 +1,17 @@
/-
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 HepLean.PerturbationTheory.Wick.Species
/-!
# Feynman diagrams
This file currently contains a lighter implmentation of Feynman digrams than can be found in
`HepLean.PerturbationTheory.FeynmanDiagrams.Basic`. Eventually this will superseed that file.
The implmentation here is done in conjunction with Wicks species etc.
This file is currently a stub.
-/

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@ -11,8 +11,6 @@ import HepLean.PerturbationTheory.Wick.Species
Currently this file is only for an example of Wick strings, correpsonding to a
theory with two complex scalar fields. The concepts will however generalize.
This file is currently a stub.
We will formally define the operator ring, in terms of the fields present in the theory.
## Futher reading
@ -46,6 +44,8 @@ informal_definition WickAlgebra where
Asympotic states:
- `φc : 𝓔 × SpaceTime → A`. The creation asympotic state (incoming).
- `φd : 𝓔 × SpaceTime → A`. The destruction asympotic state (outgoing).
Subject to the conditions:
...
"
physics :≈ "This is defined to be an
abstraction of the notion of an operator algebra."
@ -88,6 +88,17 @@ informal_definition normalOrder where
end WickMonomial
informal_definition asymptoicContract where
math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator [φd(i), ψ(j)]."
ref :≈ "See e.g. http://www.dylanjtemples.com:82/solutions/QFT_Solution_I-6.pdf"
informal_definition contractAsymptotic where
math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator [ψ(i), φc(j)]."
informal_definition asymptoicContractAsymptotic where
math :≈ "Given two `i j : 𝓔 × SpaceTime`, the super-commutator
[φd(i), φc(j)]."
informal_definition contraction where
math :≈ "Given two `i j : 𝓔 × SpaceTime`, the element of WickAlgebra
defined by subtracting the normal ordering of `ψ i ψ j` from the time-ordering of