Boson-fermion mapping of collective fermion-pair algebras

We construct finite Dyson boson-fermion mappings of general collective algebras extended by single-fermion operators. A key element in the construction is the implementation of a similarity transformation which transforms boson-fermion images obtained directly from the supercoherent state method. In addition to the general construction, we give detailed applications to SO(2N), SU(l+1), SO(5), and SO(8) algebras.Comment: 22 pages, latex, no figure

On Problems of the Lagrangian Quantization of W3-gravity

We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.Comment: 18 pages, no figure