In this paper some properties of the irreducible multiplets of representation for the N = (p, q) -extended supersymmetry in one dimension are discussed. Essentially two results are here presented. At first a peculiar property of the one dimension is exhibited, namely that any multiplet containing 2d (d bosonic and d fermionic) particles in M different spin states, is equivalent to a {d, d} multiplet of just 2 spin states (all bosons and all fermions being grouped in the same spin). Later, it is shown that the classification of all multiplets of this kind carrying an irreducible representation of the N -extended supersymmetry is in one-to-one correspondence with the classification of real-valued Clifford Γ-matrices of Weyl type. In particular, p + q is mapped into D, the space-time dimensionality, while 2d is determined to be the dimensionality of the corresponding Γ-matrices. The implications of these results to the theory of spinning particles are analyzed. *
We construct the Lagrangian description of arbitrary integer higher spin massless fields on the background of the D -dimensional anti -de Sitter space. The operator constraints in auxiliary Fock space corresponding to subsidiary conditions for irreducible unitary massless representations of the D -dimensional anti -de Sitter group are formulated. Unlike flat space, the algebra of the constraints turns out to be nonlinear and analogous to the W 3 algebra. We construct the nilpotent BRST charge for this nonlinear algebra and derive on its basis the correct field content and gauge invariant action describing the consistent arbitrary integer spin field dynamics in AdS
We develop the BRST approach to Lagrangian formulation for all massless halfinteger higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any spin is given. It is shown that in fermionic case the higher spin field model is a reducible gauge theory and the order of reducibility grows with the value of spin. No off-shell constraints on the fields and the gauge parameters are used. We prove that in four dimensions after partial gauge fixing the Lagrangian obtained can be transformed to Fang-Fronsdal form however, in general case, it includes the auxiliary fields and possesses the more gauge symmetries in compare with Fang-Fronsdal Lagrangian. As an example of general procedure, we derive the new Lagrangian for spin 5/2 field containing all set of auxiliary fields and gauge symmetries of free fermionic higher spin field theory.
The Lagrangian description of irreducible massless representations of the Poincaré group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is adopted to the systems of second-class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules. * 731 Mod. Phys. Lett. A 2001.16:731-746. Downloaded from www.worldscientific.com by GEORGE WASHINGTON UNIVERSITY on 02/08/15. For personal use only.
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