  The Faddeev-Popov rules for quantization of theory with gauge group are
generalized for case of nvariance of quantum actions, $S_N$, on N-parametric
Abelian SUSY transformations with odd parameters $\lambda_p$, p=1,..,N and
anticommuting generators $s_p$, for N=3,4 implying substitution of ghost fields
N-plet, $C^p$ multipled on $\lambda_p$, instead of the parameter, $\xi$, of
gauge transformations. Total configuration spaces for quantum theory of the
same classical model coincide for N=3 ,4 cases. For N=3 transformations the
superspace of irrep includes in addition 3 ghost $C^p$, 3 even $B^{pq}$ and odd
$\hat{B}$ fields for p,q=1-3. It is shown for quantum action $S_{3}$ the
gauge-fixing by adding to classical action of N=3-exact term requires 1
antighost $\bar{C}$, 3 even $B^{p}$ 3 odd $\hat{B}{}^p$ and Nakanishi--Lautrup
fields. Action of N=3 transformations on the latter fields is found. The
transformations appear by N=3 BRST ones for the vacuum functional, $Z_3(0) $.
It is shown, the configuration space appears by irrep superspace for fields
$\Phi_4$ for N=4- transformations containing in addition to $A^\mu$: (4+6+4+1)
ghost-antighost $C^r$, even $B^{rs}$, odd $\hat{B}{}^r $ fields and B. Action
$S_4$ is constructed by adding to classical action of N=4-exact with gauge
boson $F_4$ as compared to gauge fermion $\Psi_3$ for N=3 case. Procedure is
valid for any admissible gauge. The equivalence with $N=1$ BRST-invariant
quantization method is explicitly found. Finite N=3,4 BRST transformations are
derived from algebraic transformations. Respective Jacobians for
field-dependent parameters are calculated. They imply the presence of
corresponding modified Ward identity to be reduced to new (usual) Ward
identities for constant parameters and describe the problem of
gauge-dependence. Introduction into diagrammatic Feynman techniques for N=3,4
cases is suggested.
