Manuscript XX-B@1 · XX-B.tex · section · 56d708a5

Bosonic and ghost contractions

Normalized Hadamard contraction data › Bosonic and ghost contractions · lines 1335–1361

XX-B@1#eq:Wfull

The smooth freedom in these choices is declared input freedom. It is not a cosmological state-selection theorem.

The auxiliary field is realized on the free equations as $B = - r F z$ . Define

W_{ev} = (W_{B} - r F W_{B} - r W_{B} F^{†} r^{2} F W_{B} F^{†}), W_{odd} = (0 W_{Q} - W_{Q} 0) .

Mixed even–odd contractions are zero. For ghosts use

c^{*} = c, c ˉ^{*} = - c ˉ .

This convention makes the displayed odd contractions compatible with the adjoint.

Displayed formulas in this passage

XX-B@1#eq:Wfull · line 1342
$W_{ev} = (W_{B} - r F W_{B} - r W_{B} F^{†} r^{2} F W_{B} F^{†}), W_{odd} = (0 W_{Q} - W_{Q} 0) .$
unlabeled · line 1356
$c^{*} = c, c ˉ^{*} = - c ˉ .$