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Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces
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, , from a total superalgebra of constraints, second, in
self-consistent way by means of finding BRST-extended initial off-shell
algebraic constraints, . In both cases, the latter constraints
supercommute on the constraint surface with constrained BRST and spin
operators . The closedness of the superalgebra guarantees that the final gauge-invariant LF is compatible with
off-shell constraints imposed on field and gauge parameter
vectors of Hilbert space not depending from the ghosts and conversion auxiliary
oscillators related to , 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.Comment: 55 pages, typos corrected, published version; footnote 1 added, typo
in (3.15) correcte
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