Research proof index

The mean energy can be expressed as a ratio of integrals.

Fundamental relation between thermodynamic and differential entropy: S_thermo = S_diff - kB * dof * log h.

If Fermat's Last Theorem is true for primes p ≥ 5, then FLT is true.

The commutator of the annihilation part of a field operator with a normal ordered list of field operators can be decomposed into the sum of the commutators of the annihilation part with each element of the list of field operators, i.e. [anPart φ, 𝓝(φ₀…φₙ)]ₛ= ∑ i, 𝓢(φ, φ₀…φᵢ₋₁) • [anPart φ, φᵢ]ₛ * 𝓝(φ₀…φᵢ₋₁φᵢ₊₁…φₙ).

For a field specification 𝓕, an element φ of 𝓕.CrAnFieldOp, a list φs of 𝓕.CrAnFieldOp, the following relation holds [φ, 𝓝(φ₀…φₙ)]ₛ = ∑ i, 𝓢(φ, φ₀…φᵢ₋₁) • [φ, φᵢ]ₛ * 𝓝(φ₀…φᵢ₋₁φᵢ₊₁…φₙ). The proof of this result ultimately goes as follows - The definition of normalOrder is used to rewrite 𝓝(φ₀…φₙ) as a scalar multiple of a `ofCrAnList...

Within a proto-operator algebra we have that φ * 𝓝ᶠ(φ₀φ₁…φₙ) = 𝓝ᶠ(φφ₀φ₁…φₙ) + [anpart φ, 𝓝ᶠ(φ₀φ₁…φₙ)]ₛF.