English

Algebraic quantum kinematics and SR-selection

Quantum Physics 2026-04-30 v1 General Relativity and Quantum Cosmology Mathematical Physics math.MP

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 C2\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=ωE=\hbar\omega, and the spin spectrum ±\pm\hbar as theorems. (ii)~The constants cc and \hbar play non-interchangeable roles: cc is intrinsic to each Fourier-conjugate space, while \hbar 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-III1\mathrm{III}_1 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.

Keywords

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

R2 v1 2026-07-01T12:40:27.927Z