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|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 η₀ langle χ^{Ψ 0}_tot|c big| Q_c|totbig| χ^{Ψ 0}_tot|crangle. 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.