Research proof index

Given two pure tensors p1 : Pure S c and p2 : Pure S c, prodP p p2 is the tensor product of those tensors returning an element in Pure S (Sum.elim c c1 ∘ ⇑finSumFinEquiv.symm). -/ def Pure.prodP {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} (p1 : Pure S c) (p2 : Pure S c1) : Pure S (Fin.append c c1) := Fin.addCases (fun i => LinearEquiv.cast (R := k)...

Double basis expansion of an element of a tensor product M ⊗[k] M₂ of two Tensorial one-index spaces. Given bases b, b2 of M, M₂ coming from the single-index tensor bases, every x : M ⊗[k] M₂ is the double sum over i, j of the iterated evaluation coefficient toField (evalT 0 j (evalT 0 i (toTensor x))) times b i ⊗ₜ b2 j.

The unit tensor is symmetric on dualing the color.

Product rule for the time derivative of a product of matrix-valued functions.

The time derivative commutes with transpose.

A lemma invalidating the step in https://arxiv.org/pdf/hep-ph/0605184 leading to equation (4.4).