Manuscript IX-E@1 · IX-E.tex · section · 8f8d5e7f

Free domain and word

Prerequisites and entering state › Free domain and word · lines 326–361

IX-E@1#eq:word

The inherited algebraic tensor domains are

D_{first} D_{second} D_{new} D_{decl} = (B \otimes W) + (W \otimes B), = (L \otimes B) + (B \otimes R), = D_{first} + D_{second}, D_{old} = P_{mc} \otimes P_{mc}, = D_{new} + D_{old}, D_{new} \cap D_{old} = {0} .

The two associations of the inherited word agree with

A_{c} (f, g, f^{'}) = B_{f} W_{g} B_{f^{'}} + ℏ (G_{12} + G_{13} + G_{23}) + ℏ^{2} (G_{12, 23} + G_{12, 13} + G_{13, 23}) + ℏ^{3} N_{c} (f, g, f^{'}) 1.

Equation (eq:word) is free-word coherence. It supplies neither a binary time-ordered extension nor causal factorization.

No closure under intermediate multiplication is imported. In particular, an arbitrary expression

(F ⋆_{c} G) \otimes H

need not belong coefficientwise to the declared free domain.

Displayed formulas in this passage

unlabeled · line 329
$D_{first} D_{second} D_{new} D_{decl} = (B \otimes W) + (W \otimes B), = (L \otimes B) + (B \otimes R), = D_{first} + D_{second}, D_{old} = P_{mc} \otimes P_{mc}, = D_{new} + D_{old}, D_{new} \cap D_{old} = {0} .$
IX-E@1#eq:word · line 342
$A_{c} (f, g, f^{'}) = B_{f} W_{g} B_{f^{'}} + ℏ (G_{12} + G_{13} + G_{23}) + ℏ^{2} (G_{12, 23} + G_{12, 13} + G_{13, 23}) + ℏ^{3} N_{c} (f, g, f^{'}) 1.$
unlabeled · line 357
$(F ⋆_{c} G) \otimes H$