A General Solution of the Master Equation for a Class of First Order Systems

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the interaction part satisfies some properties, it is possible to give the solution of the master equation in a very simple way. To clarify the general procedure we discuss its application to Yang-Mills theory, massive (abelian) theory in the Stueckelberg formalism, relativistic particle and to the self-interacting antisymmetric tensor field.Comment: 11 pages, IC/92/42

A General Solution of the BV-Master Equation and BRST Field Theories

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization.Comment: 11 pages, Plain Latex (latex twice), IC/93/9

BV and BFV Formulation of a Gauge Theory of Quadratic Lie Algebras in 2-d and a Construction of W3 Topological Gravity

The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. $W_3$ algebra, formulated in terms of a continuous variable is emploied in the mentioned gauge theory to construct a $W_3$ topological gravity. Moreover, its gauge fixing is briefly discussed.Comment: 12 pages, Plain Latex (latex twice

Consistent Interactions in terms of the Generalized Fields Method

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method of solving the Batalin-Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to spin-1 gauge field in 3 and 4 dimensions, to free BF theory in 2-d and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.Comment: to appear in IJMPA, extended and some refs. adde