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

Gauge fermion and ghost normalization

Stage 1: the normalized free auxiliary–ghost multiplet › Gauge fermion and ghost normalization · lines 658–681

X-G-ST@1#eq:Psi0, X-G-ST@1#eq:S0

Take the gauge fermion

Ψ_{0} = \int c ˉ_{μ} ((C r)^{μ} - b^{μ}) d^{4} x .

The word “fermion” here denotes an odd gauge-fixing functional; no physical spinor is introduced. The free action is

S_{0} = \frac{1}{2} ⟨ r, A r ⟩ - \frac{1}{2} ⟨ ϕ, P_{m} ϕ ⟩ + s_{0} Ψ_{0}, s_{0} Ψ_{0} = \int (b_{μ} (C r)^{μ} - b_{μ} b^{μ} - c ˉ_{μ} □ c^{μ}) d^{4} x .

As elsewhere, these are local actions with compact variations.

Displayed formulas in this passage

X-G-ST@1#eq:Psi0 · line 661
$Ψ_{0} = \int c ˉ_{μ} ((C r)^{μ} - b^{μ}) d^{4} x .$
X-G-ST@1#eq:S0 · line 668
$S_{0} = \frac{1}{2} ⟨ r, A r ⟩ - \frac{1}{2} ⟨ ϕ, P_{m} ϕ ⟩ + s_{0} Ψ_{0}, s_{0} Ψ_{0} = \int (b_{μ} (C r)^{μ} - b_{μ} b^{μ} - c ˉ_{μ} □ c^{μ}) d^{4} x .$