Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces
Abstract
We study the properties of nonlinear superalgebras A and algebras Ab arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations D(E0,s1,s2) in AdSd-spaces and the sets of operators that form A and Ab, respectively, for fermionic, si=ni+1/2, and bosonic, si=ni, ni ∈ N0, i=1,2, HS fields characterized by a Young tableaux with two rows. We consider a method of constructing the Verma modules VA, VAb for A, Ab and establish a possibility of their Fock-space realizations in terms of formal power series in oscillator operators which serve to realize an additive conversion of the above (super)algebra (A) Ab, containing a set of 2nd-class constraints, into a converted (super)algebra Abc = Ab + A'b (Ac = A + A'), containing a set of 1st-class constraints only. For the algebra Abc, we construct an exact nilpotent BFV--BRST operator Q' having nonvanishing terms of 3rd degree in the powers of ghost coordinates and use Q' to construct a gauge-invariant Lagrangian formulation (LF) for HS fields with a given mass m (energy E0(m)) and generalized spin s=(s1,s2). LFs with off-shell algebraic constraints are examined as well.