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

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