  We construct a gauge-fixing procedure in the path integral for gravitational
models with branes and boundaries. This procedure incorporates a set of gauge
conditions which gauge away effectively decoupled diffeomorphisms acting in the
$(d+1)$-dimensional bulk and on the $d$-dimensional brane. The corresponding
gauge-fixing factor in the path integral factorizes as a product of the bulk
and brane (surface-theory) factors. This factorization underlies a special bulk
wavefunction representation of the brane effective action. We develop the
semiclassical expansion for this action and explicitly derive it in the
one-loop approximation. The one-loop brane effective action can be decomposed
into the sum of the gauge-fixed bulk contribution and the contribution of the
pseudodifferential operator of the brane-to-brane propagation of quantum
gravitational perturbations. The gauge dependence of these contributions is
analyzed by the method of Ward identities. By the recently suggested method of
the Neumann-Dirichlet reduction the bulk propagator in the semiclassical
expansion is converted to the Dirichlet boundary conditions preferable from the
calculational viewpoint.
