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BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields

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 $\overline{C}, \overline{\mathcal{P}}, λ, π$, 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 $Ψ_H$ as a kernel of the gauge-fixing BRST-BV Fermion functional $Ψ$, 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 $Ψ$ in a total BRST-BV action $S^Ψ_{0|s} = \int d η_0 \langle χ^{Ψ 0}_{\mathrm{tot}|c} \big| Q_{c|\mathrm{tot}}\big| χ^{Ψ 0}_{\mathrm{tot}|c}\rangle$. We use a gauge condition which depends on two gauge parameters, thereby extending the case of $R_ξ$-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.