BRST-BV quantum actions for constrained totally-symmetric integer HS fields

Abstract

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 Qc|tot with non-minimal Hamiltonian BFV oscillators C‾,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 ΨH 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 S0|sΨ=∫dη0〈χtot|cΨ0|Qc|tot|χtot|cΨ0〉. We use a gauge condition which depends on two gauge parameters, thereby extending the case of Rξ-gauges. For triplet and doublet 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.