GENERAL-SOLUTION TO THE QUANTUM MASTER EQUATION IN THE FINITE-DIMENSIONAL CASE

The general solution to the quantum master equation (and its Sp(2) sym metric counterpart) is explicitly constructed in the case of a finite number of variables. it is shown that the finite-dimensional solution is physically trivial and, therefore, cannot be directly extended to a local field theory. Thus, the locality condition is important in obta ining nontrivial physical results when quantizing gauge field theories in the field-antifield formalism.