Reformulation of Boundary BF Theory Approach to Statistical Explanation of the Entropy of Isolated Horizons

It is shown in this paper that the symplectic form for the system consisting of $D$-dimensional bulk Palatini gravity and SO$(1,1)$ BF theory on an isolated horizon as a boundary just contains the bulk term. An alternative quantization procedure for the boundary BF theory is presented. The area entropy is determined by the degree of freedom of the bulk spin network states which satisfy a suitable boundary condition. The gauge-fixing condition in the approach and the advantages of the approach are also discussed.