Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces

Abstract

BRST-BFV method for constrained Lagrangian formulations (LFs) for (ir)reducible half-integer HS Poincare group representations in Minkowski space is suggested. The procedure is derived by 2 ways: from the unconstrained BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting the second-class constraints, $\widehat{O}_\alpha=(\widehat{O}_a, \widehat{O}^+_a)$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, $\widehat{O}_a$. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST $Q_C$ and spin operators $\sigma^i_C$. The closedness of the superalgebra $Q_C, \widehat{O}_a, \sigma^i_C$ guarantees that the final gauge-invariant LF is compatible with off-shell constraints $\widehat{O}_a$ imposed on field and gauge parameter vectors of Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to $\widehat{O}_a$, in comparison with vectors for unconstrained BRST-BFV LF. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained LFs for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with Fang-Fronsdal formulation for constrained totally-symmetric HS field. The triplet and unconstrained quartet LFs for the latter field and gauge-invariant constrained Lagrangians for a massive field of spin n+1/2 are derived. A concept of BRST-invariant second-class constraints for a general dynamical system with mixed-class constraints is suggested.