General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields

Understand

We construct a Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach.

• Starting with a description of bosonic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system.
• For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables.
• We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin.