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feat: Add Wick terms

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jstoobysmith 2025-02-05 08:52:14 +00:00
parent 7d9e6af80c
commit 2e82f842a2
12 changed files with 634 additions and 553 deletions
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3
HepLean/PerturbationTheory/WickContraction/Basic.lean
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@ -3,8 +3,7 @@ Copyright (c) 2025 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.FieldOpAlgebra.NormalOrder
import HepLean.Mathematics.List.InsertIdx
import HepLean.PerturbationTheory.FieldSpecification.Basic
/-!
# Wick contractions

5
HepLean/PerturbationTheory/WickContraction/TimeContract.lean
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@ -34,8 +34,7 @@ noncomputable def timeContract {φs : List 𝓕.FieldOp}
This result follows from the fact that `timeContract` only depends on contracted pairs,
and `(φsΛ ↩Λ φ i none)` has the 'same' contracted pairs as `φsΛ`. -/
@[simp]
lemma timeContract_insertAndContract_none
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
lemma timeContract_insertAndContract_none (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
(φsΛ ↩Λ φ i none).timeContract = φsΛ.timeContract := by
rw [timeContract, insertAndContract_none_prod_contractions]
@ -78,7 +77,7 @@ lemma timeContract_empty (φs : List 𝓕.FieldOp) :
open FieldStatistic
lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_lt
lemma timeContract_insertAndContract_some_eq_mul_contractStateAtIndex_lt
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
(ht : 𝓕.timeOrderRel φ φs[k.1]) (hik : i < i.succAbove k) :