  In this paper we construct path integral representations of the boundary
states in some special backgrounds such as the U(1) gauge field background, the
linear dilaton background and the open string tachyon background. The initial
purpose of this paper is to construct a general solution of the boundary
conformal field theory with the analytical approach, mainly for the constraint
equations$(L_{n}-\tilde{L}_{-n}) |B > =0 $ are difficult to be solved to obtain
the solution represented by string modes from the pure algebraic approach.
However in the path integral representation it is easy transforming those
algebraic equations into the differential equations which can be solved.
Another purpose of this paper is to try to explore an open question. we do not
know how to construct an exact theory of D-branes in the general background
until now. However many recent researches show the boundary state description
indeed seizes some fundamental features of D-branes in the rather special
backgrounds. Since the general background field effects can be easily
introduced in the path integral representation, we argue that path integral
representation of the boundary state should provide an exact description of D
branes in the general backgrounds.

High Energy Physics - Theory