Manuscript XI-B@1 · XI-B.tex · section · 063b989e

The normalization of the ghost

One gauge fermion and the auxiliary multiplet › The normalization of the ghost · lines 440–464

XI-B@1#eq:R, XI-B@1#eq:s

Define

R c = \frac{1}{2} K c, (R c)_{μν} = \partial_{(μ} c_{ν)} .

Thus the requested parenthesis convention is retained. XI-A's variation $K ξ$ is recovered by setting $c = 2 ξ$ . This fixes a ghost normalization; it introduces neither a new metric gauge condition nor a gauge-parameter family.

The free odd derivation is specified on independent fields by

s_{0} γ = R c, s_{0} ϕ = 0, s_{0} c = 0, s_{0} c ˉ_{μ} = i b_{μ}, s_{0} b_{μ} = 0.

It commutes with spacetime derivatives and raises ghost number by one. Its action on products is the graded Leibniz rule.

Displayed formulas in this passage

XI-B@1#eq:R · line 443
$R c = \frac{1}{2} K c, (R c)_{μν} = \partial_{(μ} c_{ν)} .$
XI-B@1#eq:s · line 454
$s_{0} γ = R c, s_{0} ϕ = 0, s_{0} c = 0, s_{0} c ˉ_{μ} = i b_{μ}, s_{0} b_{μ} = 0.$

Nearby in this section

lemma: Lemma: Off-shell nilpotence