Using the method of expanding the algebraic constraint, we calculated the a
ctions of the vacuum Hamiltonian constraint on the extended diffeomorphism
invariant knot states( * phi(G))(2),( * phi(G))(3) and phi(G) * J(2). We ob
tain that they are inhomogeneous under the vacuum Hamiltonian constraint. F
inally, the cancellation of the inhomogeneous property of the state( * phi(
G))(2) is given.