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Project-declaredLean 4.32.0

Mul static Wick Term eq sum

WickContraction.mul_staticWickTerm_eq_sum

Plain-language statement

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, the following relation holds φ * φsΛ.staticWickTerm = ∑ k, (φsΛ ↩Λ φ 0 k).staticWickTerm where the sum is over all k in Option φsΛ.uncontracted, so k is either none or some k. The proof proceeds as follows: - ofFieldOp_mul_normalOrder_ofFieldOpList_eq_sum is used to e...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Static Wick Term insert zero some

WickContraction.staticWickTerm_insert_zero_some

Plain-language statement

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, and a k in φsΛ.uncontracted, (φsΛ ↩Λ φ 0 (some k)).wickTerm is equal to the product of - the sign 𝓢(φ, φ₀…φᵢ₋₁) - the sign φsΛ.sign - φsΛ.staticContract - s • [anPart φ, ofFieldOp φs[k]]ₛ where s is the sign associated with moving `...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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