Abstract
New construction of $4D$ dynamical space-time (DST) has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the fundamental notion of generalized coherent state (GCS) of N-level system and the geometry of unitary group $SU(N)$ acting in state space $C^N$. Neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction. Morphogenesis of the ``field shell"-lump of GCS and its dynamics have been studied for $N=2$ in DST. The main technical problem is to find non-Abelian gauge field arising from conservation law of the local Hailtonian vector field. The last one may be expressed as parallel transport of local Hamiltonian in projective Hilbert space $CP(N-1)$. Co-movable local ``Lorentz frame" being attached to GCS is used for qubit encoding result of comparison of the parallel transported local Hamiltonian in infinitesimally close points. This leads to quasi-linear relativistic field equations with soliton-like solutions for ``field shell" in emerged DST. The terms ``comparison" and ``encoding" resemble human's procedure, but here they have objective content realized in invariant quantum dynamics. The dynamical motion of the lump in DST may be associated with ``kinesis" time whereas the evolution parameter describing morphogenesis of GCS evolving in $CP(N-1)$, may be naturally identified with ``metabole" time.
Peter Leifer