  The Hamiltonian constraint Hc = NH = 0, defines a diffeomorphic structure on
spatial manifolds by the lapse function N in general theory of relativity.
However, it is not manifest in Lanczos-Lovelock gravity, since the expression
for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a
branch function of momentum. Here we propose an extended theory of
Lanczos-Lovelock gravity to construct a unique Hamiltonian in its
minisuperspace version, which results in manifest diffeomorphic invariance and
canonical quantization.
