A constrained BRST-BV Lagrangian formulation for totally symmetric massless HS fields in a $d$-dimensional Minkowski space is extended to a non-minimal constrained BRST-BV Lagrangian formulation by using a non-minimal BRST operator $Q_{ c|\mathrm{ tot}}$ with non-minimal Hamiltonian BFV oscillators $\overline{ C}, \overline{ \mathcal{ P}}, \lambda, \pi$, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion $\Psi_H$ as a kernel of the gauge-fixing BRST-BV Fermion functional $\Psi$, manifesting the concept of BFV-BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion $\Psi$ in a total BRST-BV action $S^{ \Psi}_{ 0|s} = \int d \eta_0 \langle \chi^{ \Psi{ } 0}_{ \mathrm{ tot}|c} \big| Q_{ c|\mathrm{ tot}}\big| \chi^{ \Psi{ } 0}_{ \mathrm{ tot}|c}\rangle$. We use a gauge condition which depends on two gauge parameters, thereby extending the case of $R_\xi$-gauges. For triplet and duplet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Green's functions, BRST symmetry transformations are suggested and Ward identities are obtained.
Categories: hep-th math-ph math.DS math.MP quant-ph