On generalized gauge fixing in the field-antifield formalism

We consider the problem of covariant gauge fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the quantum master equation. Analogous to the gauge-generating algebra of the action W, we analyze the possibility of having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing algebra of the so-called first stage in full detail and generalize to arbitrary stages. The associated “square root” measure contributions are worked out from first principles, with or without the presence of antisymplectic second-class constraints. Finally, we consider an W-X alternating multi-level generalization.