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

• URL: http://arxiv.org/abs/2010.15741v4
• Date: Tue, 2 Mar 2021 01:24:33 GMT
• Title: BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields
• Authors: \v{C}estmir Burd\'ik, Alexander A. Reshetnyak
• Abstract summary: A non-minimal constrained BRST-BV Lagrangian formulation is presented for totally symmetric massless HS fields in a $d$-dimensional Minkowski space. A Fock-space quantum action 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.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $Q_{c|\mathrm{tot}}$ 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.

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