Quantum Geometry of the Dynamical Space-time

Abstract

Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time coordinates. The fate of quantum system modeled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent) space-time arises only at the stage of the quantum "yes/no" measurement. The quantum measurement of the gauge ``field shell'' of the generalized coherent state is described in terms of the affine parallel transport of the local dynamical variables in $CP(N-1)$.