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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations Quantum Simulation

Algebraic quantum kinematics and SR-selection

arXiv
Authors: Leonardo A. Pachon

Year

2026

Paper ID

56622

Status

Preprint

Abstract Read

~2 min

Abstract Words

219

Citations

0

Abstract

We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity. Three structural facts organize the framework. (i) The photon sector of free QED is a transparent realization: classical Fourier--Maxwell theory supplies a complex Hilbert-space scaffold inner product, symplectic form, Schrödinger-form mode equation, polarization $mathbb{C}2$ with no quantum input, and a single canonical commutator with scale hbar on the mode amplitudes promotes it to single-photon QED, with photon indivisibility, the Planck relation E=hbarω, and the spin spectrum pmhbar as theorems. (ii) The constants c and hbar play non-interchangeable roles: c is intrinsic to each Fourier-conjugate space, while hbar acts between them, converting kinematic phase rates into dynamical observables. (iii) Lifting the framework to a Haag--Kastler net with sharper-than-equal-time microcausality and positive-energy spectrum is structurally obstructed in the Galilean case; we state this as the SR-selection conjecture and identify three strands of evidence (Hegerfeldt spreading; absence of a known Galilean multi-particle resolution; Reeh--Schlieder failure on Galilean Haag--Kastler nets), the third established as a precise no-go theorem in the second paper of the series. The framework's modular content Tomita--Takesaki, Bisognano--Wichmann, Unruh as KMS, type-$III1$ universality is collected as the algebraic substrate on which the curved-background, dynamical-metric, and crossed-product extensions of the third through sixth papers operate.

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  • We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity.

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