Algebraic quantum kinematics and SR-selection
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, Schr\"odinger-form mode equation, polarization ) with no quantum input, and a single canonical commutator with scale on the mode amplitudes promotes it to single-photon QED, with photon indivisibility, the Planck relation , and the spin spectrum as theorems. (ii)~The constants and play non-interchangeable roles: is intrinsic to each Fourier-conjugate space, while acts \emph{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- 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.
Cite
@article{arxiv.2604.26267,
title = {Algebraic quantum kinematics and SR-selection},
author = {Leonardo A. Pachon},
journal= {arXiv preprint arXiv:2604.26267},
year = {2026}
}
Comments
18 pages, 2 figures