1211.1273 (Alexander A. Reshetnyak)

General Lagrangian Formulation for Higher Spin Fields with Arbitrary
Index Symmetry. 2. Fermionic fields    [PDF]

Alexander A. Reshetnyak

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having $k$ rows, on a basis of the BRST-BFV approach developed for bosonic fields in our first paper [Nucl. Phys. B862 (2012) 270, [arXiv:1110.5044[hep-th]]. Starting with a description of fermionic 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. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to $osp(k|2k)$ superalgebra, 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 fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for fermionic fields subject to arbitrary Young tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model of massless rank-3 spin-tensor field of spin $(5/2,3/2)$ with first-stage reducible gauge symmetries and non-gauge Lagrangian for massive rank-3 spin-tensor field of spin $(5/2,3/2)$.

View original: http://arxiv.org/abs/1211.1273