Time Contract of time Order Rel
FieldSpecification.WickAlgebra.timeContract_of_timeOrderRel
Plain-language statement
For a field specification ๐, and ฯ and ฯ elements of ๐.FieldOp, if ฯ and ฯ are time-ordered then timeContract ฯ ฯ = [anPart ฯ, ofFieldOp ฯ]โ.
Exact Lean statement
lemma timeContract_of_timeOrderRel (ฯ ฯ : ๐.FieldOp) (h : timeOrderRel ฯ ฯ) :
timeContract ฯ ฯ = [anPart ฯ, ofFieldOp ฯ]โFormal artifact
Lean source
lemma timeContract_of_timeOrderRel (ฯ ฯ : ๐.FieldOp) (h : timeOrderRel ฯ ฯ) : timeContract ฯ ฯ = [anPart ฯ, ofFieldOp ฯ]โ := by conv_rhs => rw [ofFieldOp_eq_crPart_add_anPart] rw [map_add, superCommute_anPart_anPart, superCommute_anPart_crPart] simp only [timeContract, Algebra.smul_mul_assoc, add_zero] rw [timeOrder_ofFieldOp_ofFieldOp_ordered h] rw [normalOrder_ofFieldOp_mul_ofFieldOp] rw [ofFieldOp_eq_crPart_add_anPart, ofFieldOp_eq_crPart_add_anPart] simp only [mul_add, add_mul] abel_nf- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QFT/PerturbationTheory/WickAlgebra/TimeContraction.lean:42-52
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