Manuscript X-L-ST@1 · X-L-ST.tex · proposition · 20a32a22
Proposition: The classical master residual
A restricted classical BV construction › Action input and signed Hamiltonian lift · lines 847–871 · proof included or linked
X-L-ST@1#prop:masterresidual, X-L-ST@1#eq:curvature
On the declared variational domain,
The residual has parity one and ghost number one. It is field-dependent and antifield-independent.
It need not vanish merely because .
Proof. Field-only functionals have zero mutual antibracket. Lemma lem:kinmaster removes the kinematic self-bracket. The two mixed brackets coincide because both Hamiltonians are even, and give . The other two identities are the odd Jacobi identities. The parity and ghost-number statements follow from the degree of the odd bracket.
Displayed formulas in this passage
X-L-ST@1#eq:curvature · line 850