Morphogenesis and dynamics of quantum state

TL;DR

This paper proposes a novel 4D dynamical space-time framework based on generalized coherent states and the geometry of SU(N), deriving relativistic field equations with soliton solutions without relying on traditional space-time coordinates.

Contribution

It introduces a new unification of relativity and quantum theory using GCS and SU(N) geometry, avoiding conventional notions of particles and space-time coordinates.

Findings

Derived quasi-linear relativistic field equations with soliton solutions.

Established a connection between quantum state morphogenesis and space-time dynamics.

Proposed a new conceptual framework for quantum-relativistic unification.

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.