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feat: Property of time-order w.r.t. superCommute

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jstoobysmith 2025-01-29 12:09:02 +00:00
parent a79d0f8fed
commit c2d89cc093
8 changed files with 781 additions and 8 deletions
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4
HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/Basic.lean
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@ -92,7 +92,7 @@ lemma ι_superCommute_of_annihilate_annihilate (φa φa' : 𝓕.CrAnStates)
left
use φa, φa', hφa, hφa'
lemma ι_superCommute_of_diff_statistic (φ ψ : 𝓕.CrAnStates)
lemma ι_superCommute_of_diff_statistic {φ ψ : 𝓕.CrAnStates}
(h : (𝓕 |>ₛ φ) ≠ (𝓕 |>ₛ ψ)) : ι [ofCrAnState φ, ofCrAnState ψ]ₛca = 0 := by
apply ι_of_mem_fieldOpIdealSet
simp only [fieldOpIdealSet, exists_prop, exists_and_left, Set.mem_setOf_eq]
@ -107,7 +107,7 @@ lemma ι_superCommute_zero_of_fermionic (φ ψ : 𝓕.CrAnStates)
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton] at h ⊢
rcases statistic_neq_of_superCommute_fermionic h with h | h
· simp [ofCrAnList_singleton]
apply ι_superCommute_of_diff_statistic _ _
apply ι_superCommute_of_diff_statistic
simpa using h
· simp [h]