Manuscript XX-D@1 · XX-D.tex · section · c83a526d

External one-contraction products

Native infrared conditions and the cutoff-free theorem › External one-contraction products · lines 1409–1423

XX-D@1#eq:star

This is the sufficient one-sided covariance condition used in XX-C. It is rechecked here when used.

For polynomials whose contraction is defined, the order- $ℏ$ product is

F ⋆_{W} G = F G + ℏ ⟨ F^{(1)}, W G^{(1)} ⟩ (mod ℏ^{2}) .

Displayed formulas in this passage

XX-D@1#eq:star · line 1417
$F ⋆_{W} G = F G + ℏ ⟨ F^{(1)}, W G^{(1)} ⟩ (mod ℏ^{2}) .$