Hydrogenic Bound States from Phase Holonomy, Part I

Updated Zenodo description (Part I)

Title: Hydrogenic Bound States from Phase Holonomy, Part I
Subtitle: A Derivation within Super Information Theory

Description:

Super Information Theory (SIT) introduces a real time-density scalar ρt\rho_tρt and a complex coherence field ψ=Rcoheiθ\psi = R_{\mathrm{coh}} e^{i\theta}ψ=Rcoheiθ as primitive informational degrees of freedom, and is constructed to recover ordinary quantum field theory (QFT) in a constant-background (decohered) limit. This manuscript provides a conservative derivational consistency analysis for atomic physics within that limit. Assuming that the SIT decohered regime yields a locally U(1)U(1)U(1)-invariant matter–electromagnetic sector equivalent to quantum electrodynamics, we recover the Coulomb field as the static solution of the (possibly dressed) Maxwell equations and derive the familiar inverse-square scaling Er∝1/r2E_r \propto 1/r^2Er∝1/r2 and potential ϕ∝1/r\phi \propto 1/rϕ∝1/r via Gauss’ law.

Orbital quantization is then formulated in a gauge-covariant geometric language, emphasizing connections, holonomy, and global single-valuedness. In this framework, Bohr–Sommerfeld quantization is recovered as a semiclassical limit, and the full hydrogenic spectrum is identified with that of the recovered Schrödinger or Dirac eigenvalue problem. The paper explicitly clarifies its scope and non-claims: it does not replace quantum electrodynamics within its established domain of validity. Instead, it demonstrates internal consistency of SIT with known atomic physics in the decohered limit and identifies a falsifiable pathway for SIT-specific deviations through environment-dependent dressing functions when coherence or time-density gradients become appreciable.

This work serves as Part I of a two-part analysis. A companion manuscript (Part II) addresses the deeper question of why hydrogenic bound states and quantization arise as unavoidable consequences within the full SIT dynamical framework.