Only 1 Grassmann-odd global $\epsilon$ parameter is needed in the BRST formulation even if the underlying gauge theory contains several gauge parameters.

The formal proof of the existence of a BRST formulation for an arbitrary Hamiltonian & Lagrangian gauge theory with possibly reducible and open gauge algebra was given in a series of articles by Batalin, Fradkin & Vilkovisky, cf. e.g. Ref. 1 and references therein.

Roughly speaking, the main tool in the existence proof of a Grassmann-odd nilpotent BRST symmetry of ghost number 1 is deformation of a cohomological complex of fields.

References:

1. M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994.

Only 1 Grassmann-odd global parameter $\epsilon\in \mathbb{R}^{0|1}$ is needed in the BRST formulation $\delta=\epsilon {\bf s}$ even if the underlying gauge theory contains several gauge parameters.

The formal proof of the existence of a BRST formulation for an arbitrary Hamiltonian & Lagrangian gauge theory with possibly reducible and open gauge algebra was given in a series of articles by Batalin, Fradkin & Vilkovisky, cf. e.g. Ref. 1 and references therein.

Roughly speaking, the main tool in the existence proof of a Grassmann-odd nilpotent BRST symmetry ${\bf s}$ of ghost number 1 is deformation of a cohomological complex of fields.

References:

1. M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994; chapters 9 + 10 + 17.

Only 1 Grassmann-odd global $\epsilon$ parameter is needed in the BRST formulation.

The formal proof of the existence of a BRST formulation for an arbitrary Hamiltonian & Lagrangian gauge theory with possibly reducible and open gauge algebra was given in a series of articles by Batalin, Fradkin & Vilkovisky, cf. e.g. Ref. 1 and references therein.

Roughly speaking, the main tool in the existence proof of a Grassmann-odd nilpotent BRST symmetry of ghost number 1 is deformation of a cohomological complex of fields.

References:

1. M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994.

Only 1 Grassmann-odd global $\epsilon$ parameter is needed in the BRST formulation even if the underlying gauge theory contains several gauge parameters.

The formal proof of the existence of a BRST formulation for an arbitrary Hamiltonian & Lagrangian gauge theory with possibly reducible and open gauge algebra was given in a series of articles by Batalin, Fradkin & Vilkovisky, cf. e.g. Ref. 1 and references therein.

Roughly speaking, the main tool in the existence proof of a Grassmann-odd nilpotent BRST symmetry of ghost number 1 is deformation of a cohomological complex of fields.

References:

1. M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994.