Horizon-Restricted Leading Soft QED as Open Quantum System

2026-07-08

AI Summary

This work addresses the decoherence of charged superselection sectors induced by black hole horizons by modeling the system as an open quantum system. It restricts soft QED to an exterior algebra and employs the Feynman–Vernon influence functional to capture the inequivalent histories monitored by the horizon, thereby constructing a completely positive Schur channel that governs the decoherence dynamics. The study innovatively proposes a charged qutrit interferometer based on Bargmann holonomies in the soft phase space near the horizon, yielding a measurable holonomy phase identified with the symplectic area of a soft phase-space triangle. It further establishes constraints from Gram positivity, a quantum erasure bound, and a non-Markovianity criterion. This framework enables falsifiable experimental tests of scaling laws for soft/hard processes, common-mode structures, and triangulation invariants, transcending the conventional two-path visibility paradigm.

Abstract

I formulate black-hole-horizon-induced decoherence of charged branch codes as the leading-soft QED restricted to an exterior algebra, formulated as an open quantum system. The fixed-history Feynman--Vernon identity ${\cal F}[J,J]=1$ remains exact. Decoherence enters through the unequal-history influence factor that survives exterior monitoring and belongs to the complementary horizon output. In the coherent eikonal regime, I derive the completely positive Schur channel $({\cal E}_H^{(0)}ρ)_{ab}=\langleΦ_b^{H,(0)}|Φ_a^{H,(0)}\rangle \, ρ_{ab}$. The leading soft input is the eikonal factor, projected onto the horizon radiative algebra. The channel yields Gram-positivity constraints, an exterior quantum-eraser bound, finite-time non-Markovianity tests, soft/hard scaling criteria, and a charged-qutrit interferometer measuring a leading-soft Bargmann holonomy. The holonomy phase is the rephasing-invariant symplectic area of a triangle in horizon soft phase space. I show that its orientation, common-mode, triangulation, and completely positive determinant identities render falsifiable tests beyond pairwise two-path visibility.

Problem

• black hole horizon
• decoherence
• soft QED
• open quantum system
• charged branch codes

Innovation

• open quantum system
• soft QED
• decoherence
• Bargmann holonomy
• completely positive channel