  Quantum de Sitter geometry is discussed using elementary field operator
algebras in Krein space quantization from an observer-independent point of
view, {\it i.e.} ambient space formalism. In quantum geometry, the conformal
sector of the metric becomes a dynamical degree of freedom, which can be
written in terms of a massless minimally coupled scalar field. The elementary
fields necessary for the construction of quantum geometry are introduced and
classified. A complete Krein-Fock space structure for elementary fields is
presented using field operator algebras. We conclude that since quantum de
Sitter geometry can be constructed by elementary field operators, the geometry
quantum state is immersed in the Krein-Fock space and evolves in it. The total
number of accessible quantum states in the universe is chosen as a parameter of
quantum state evolution, which has a relationship with the universe's entropy.
Inspired by the Wheeler-DeWitt constraint equation in cosmology, the evolution
equation of the geometry quantum state is formulated in terms of the Lagrangian
density of interaction fields in ambient space formalism.
