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, ${\hat{O}}_{\alpha }=({\hat{O}}_a,{\hat{O}}_a^{+})$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, ${\hat{O}}_a$. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST $Q_C$ and spin operators ${\sigma }_C^i$. The closedness of the superalgebra $Q_C,{\hat{O}}_a,{\sigma }_C^i$ guarantees that the final gauge-invariant LF is compatible with off-shell constraints ${\hat{O}}_a$ imposed on field and gauge parameter vectors of Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to ${\hat{O}}_a$, 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.

55 pages, typos corrected, published version; footnote 1 added, typo in (3.15) corrected

References in corpus (15)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Quartet unconstrained formulation for massless higher spin fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• Parent form for higher spin fields on anti-de Sitter space
• Higher-Spin Theory and Space-Time Metamorphoses
• Gauge invariant Lagrangian construction for massive higher spin fermionic fields
• Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space. Fermions
• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries

Cited by in corpus (11)

• A local action for fermionic unconstrained higher spin gauge fields in (A)dS space
• BRST-BFV and BRST-BV Descriptions for Bosonic Fields with Continuous Spin on $R^{1,d-1}$
• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• BRST-BV approach for interacting higher spin fields
• Towards the structure of a cubic interaction vertex for massless integer higher spin fields
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold
• Covariant Lagrangian Cubic Interaction Vertices For Irreducible Higher Spin Fields in Minkowski Backgrounds
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II
• Towards Lagrangian dynamics for constrained mixed-symmetric interacting higher-spin fields