Manuscript X-G@1 · X-G.tex · section · 01566e14

Independent fields and the fermion

The normalized free BRST multiplet › Independent fields and the fermion · lines 559–573

X-G@1#eq:Psi0, X-G@1#eq:sPsi

Choose

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

The graded Leibniz rule and $C K = □$ give

s_{0} Ψ_{0} = \int (b_{μ} C^{μ} [h] - b_{μ} b^{μ} - c ˉ_{μ} □ c^{μ}) d^{4} x .

Displayed formulas in this passage

X-G@1#eq:Psi0 · line 562
$Ψ_{0} = \int c ˉ_{μ} (C^{μ} [h] - b^{μ}) d^{4} x .$
X-G@1#eq:sPsi · line 567
$s_{0} Ψ_{0} = \int (b_{μ} C^{μ} [h] - b_{μ} b^{μ} - c ˉ_{μ} □ c^{μ}) d^{4} x .$