Observer in Quantum Cosmology

Within the framework of the new formalism of quantum theory - the quantum principle of least action - the initial state of the universe is determined, which is an analogue of the Hartle-Hawking no-boundary wave function. The quantum evolution of the universe is modified by additional conditions in a certain compact region of space-time, which is called the observation region. Additional conditions are Noether identities related to the general covariance of the theory and internal symmetries of matter fields. The consequences of the local law of conservation of the energy-momentum tensor of matter are considered in detail. Its consequence is the deterministic nature of the motion of the energy and momentum densities of matter in the observation area. The geometric parameters of the region boundary are also determined by the deterministic motion of the matter fields inside. The choice of boundary conditions for the energy-momentum flow at the boundary serves as a mechanism for decoherence of the quantum evolution of the universe. The result of decoherence is a certain correspondence between the final state of the universe and the state of the observer in the specified region. This correspondence allows us to formulate the extremum principle in quantum cosmology, in which the action functional constructed using the final state determines the world history of the universe as the observer sees it.