Manuscript IX-D@3 · IX-D-v3.tex · remark · 3ad4586e
Remark: Spacelike separation is not a vanishing axiom
D1: domains and separate causal interfaces › Reversed and conjugate comparison domains · lines 869–882
IX-D@3#rem:spacelike
A time-ordered product need not vanish for spacelike-separated arguments. If causal factorization applies in both directions, the two free orderings must agree there; their common value need not be zero.
Even a contracted contribution may be smooth and nonzero away from coincidence. A distribution supported on a coincidence set vanishes on tests supported away from that set, so contact terms cannot account for such an off-diagonal spacelike contribution. This is consistent with the usual free and time-ordered distinction FR.