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Project-declaredLean 4.32.0 ยท mathlib@81a5d257c8e4

Time Contract of time Order Rel

FieldSpecification.WickAlgebra.timeContract_of_timeOrderRel

Plain-language statement

For a field specification ๐“•, and ฯ† and ฯˆ elements of ๐“•.FieldOp, if ฯ† and ฯˆ are time-ordered then timeContract ฯ† ฯˆ = [anPart ฯ†, ofFieldOp ฯˆ]โ‚›.

Exact Lean statement

lemma timeContract_of_timeOrderRel (ฯ† ฯˆ : ๐“•.FieldOp) (h : timeOrderRel ฯ† ฯˆ) :
    timeContract ฯ† ฯˆ = [anPart ฯ†, ofFieldOp ฯˆ]โ‚›

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma timeContract_of_timeOrderRel (ฯ† ฯˆ : ๐“•.FieldOp) (h : timeOrderRel ฯ† ฯˆ) :    timeContract ฯ† ฯˆ = [anPart ฯ†, ofFieldOp ฯˆ]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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Project-declaredLean 4.32.0

Adiabatic relation log

adiabatic_relation_log

Plain-language statement

Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Adiabatic relation Ua Ub Va Vb

adiabatic_relation_UaUbVaVb

Plain-language statement

Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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