In the Nexus Paradigm, the labeling [q.sub.n] refers to a creation of a Nexus graviton in the n-th quantum state associated with a conjugate momentum
More concretely, in the case of one degree of freedom, besides [??] and the conjugate momentum
[??], acting nontrivially in [H.sub.q], there should be [H.sub.t] where t, together with ?
where pr (i,t) is the conjugate momentum and can be determined from the relation
in terms of the conjugate momentum (p), the Hamiltonian density is
The Hamiltonian is expressed as a series expansion in terms of surface deformation coordinates and a conjugate momentum
. We considered only the lowest kinetic energy terms, so that the eigen problem for our Hamiltonian reduces to Schrodinger equation in five dimensional spaces.
Considering that the scale factor a is positive, we require that the wave function of the universe vanishes at a = 0, in order for the conjugate momentum of a to be hermitic.
The fact that a [greater than or equal to] 0 can spoil hermiticity of the conjugate momentum of [[pi].sub.a].
Technically, every symmetry selects a constant conjugate momentum since, by the Euler-Lagrange equations we get
and the existence of a constant conjugate momentum means that a cyclic variable (a symmetry) exists.