PhysLean/HepLean/PerturbationTheory/Wick/Theorem.lean
2024-12-03 09:51:09 +00:00

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/-
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
/-!
# Wick's theorem
Wick's theorem is related to a result in probability theory called Isserlis' theorem.
-/
namespace Wick
informal_lemma wicks_theorem where
math :≈ "Wick's theorem for fields which are not normally ordered."
informal_lemma wicks_theorem_normal_order where
math :≈ "Wick's theorem for which fields at the same space-time point are normally ordered."
ref :≈ "https://www.physics.purdue.edu/~clarkt/Courses/Physics662/ps/qftch32.pdf"
informal_lemma wicks_theorem_vev where
math :≈ "Wick's theorem in a vev leaving only full contractions of Wick strings left."
informal_lemma wicks_theorem_asymptotic_states where
math :≈ "Wick's theorem for a term in the Dyson series within asymptotic states
leaves only full contractions with the asymptotic states."
end Wick