Manuscript X-G-ST@1 · X-G-ST.tex · section · 3c97567f

Natural ghost equations without an interacting quantum differential

Natural ghost equations without an interacting quantum differential · lines 994–1013

The natural background fermion is

Ψ_{q ˉ} = \int J_{q ˉ} c ˉ_{μ} (C_{q ˉ}^{μ} [r] - q ˉ^{μν} b_{ν}) d^{4} x .

Since $s_{kin} q ˉ = 0$ ,

s_{kin} Ψ_{q ˉ} = \int J_{q ˉ} (b_{μ} C_{q ˉ}^{μ} [r] - b_{μ} q ˉ^{μν} b_{ν} - c ˉ_{μ} C_{q ˉ}^{μ} [L_{c} (q ˉ + κ r)]) d^{4} x .

Auxiliary elimination gives the retained bosonic background gauge fixing.

Displayed formulas in this passage

unlabeled · line 997
$Ψ_{q ˉ} = \int J_{q ˉ} c ˉ_{μ} (C_{q ˉ}^{μ} [r] - q ˉ^{μν} b_{ν}) d^{4} x .$
unlabeled · line 1004
$s_{kin} Ψ_{q ˉ} = \int J_{q ˉ} (b_{μ} C_{q ˉ}^{μ} [r] - b_{μ} q ˉ^{μν} b_{ν} - c ˉ_{μ} C_{q ˉ}^{μ} [L_{c} (q ˉ + κ r)]) d^{4} x .$