Quantum dynamics and state-dependent affine gauge fields on CP(N-1)

TL;DR

This paper explores a novel approach to quantum dynamics using affine gauge fields on complex projective space, linking quantum measurement, space-time emergence, and resolving paradoxes through local dynamical variables and affine parallel transport.

Contribution

It introduces a new framework connecting affine gauge fields with quantum state dynamics and space-time emergence, extending the understanding of quantum measurement and entanglement.

Findings

Formulation of PDEs for affine gauge potential solutions

Embedding quantum dynamics into dynamical space-time

Restoration of Lorentz invariance addressing quantum paradoxes

Abstract

Gauge fields frequently used as an independent construction additional to so-called wave fields of matter. This artificial separation is of course useful in some applications (like Berry's interactions between the "heavy" and "light" sub-systems) but it is restrictive on the fundamental level of "elementary" particles and entangled states. It is shown that the linear superposition of action states and non-linear dynamics of the local dynamical variables form an oscillons of energy representing non-local particles - "lumps" arising together with their "affine gauge potential" agrees with Fubini-Study metric. I use the conservation laws of local dynamical variables (LDV's) during affine parallel transport in complex projective Hilbert space $CP(N-1)$ for twofold aim. Firstly, I formulate the variation problem for the ``affine gauge potential" as system of partial differential equations \cite{Le1}. Their solutions provide embedding quantum dynamics into dynamical space-time whose state-dependent coordinates related to the qubit spinor subjected to Lorentz transformations of "quantum boosts" and "quantum rotations". Thereby, the problem of quantum measurement being reformulated as the comparison of LDV's during their affine parallel transport in $CP(N-1)$, is inherently connected with space-time emergences. Secondly, the important application of these fields is the completeness of quantum theory. The EPR and Schr\"odinger's Cat paradoxes are discussed from the point of view of the restored Lorentz invariance due to the affine parallel transport of local Hamiltonian of the soliton-like field.