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Osterwalder–Schrader axioms for scalar QED3_3 in the Higgs phase

Primarily AI-generated textHuman understanding: some partsmath-ph — Mathematical Physicsmath.MP — Mathematical Physicsmath.PR — Probability

Contributed by Mark Goldstein ↗, Alfredo Guevara ↗

Version 1 / Nov 12, 2026 / CC BY 4.0

Abstract

We study scalar quantum electrodynamics in three dimensions (QED3_3) in its Higgs phase: the three-dimensional lattice abelian Higgs model in unitary gauge, with the Villain action, on lattices whose spacing tends to zero with canonically scaled couplings. At each spacing we construct infinite-volume states, as limit points of the periodic states and as limits of states in finite boxes; they carry the lattice symmetries, reflection positivity and bounds uniform in the volume. For the smeared curvature and bounded functions of the density, the generating functionals converge along a subsequence of spacings to a translation-invariant limit functional with the continuity required for the Osterwalder–Schrader reconstruction. For the limits built on the box states, and on the periodic states along dyadic sequences of sides, the limit curvature field satisfies the axioms OS0–OS3, with invariance under the full Euclidean group. The cluster axiom OS4 is proved in a weak form, on almost every ergodic component. The tools are Gaussian domination of the Villain curvature, Ginibre inequalities and reflection positivity.

Author comments: Companion paper: Osterwalder–Schrader axioms for scalar QED$_3$ in the Coulomb phase. Project: https://github.com/marikgoldstein/scalar-qed-existence

Provenance statement

This paper and its companion represent verified output from our scalar-qed-existence project (https://github.com/marikgoldstein/scalar-qed-existence), generated via agent orchestration. The purpose of the project is to finalize King's treatment of the theory, which already provides insight into the proof. We are currently in the process of digesting the results.

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Version history

  1. v1 · 205 pagesSubmitted by Mark GoldsteinCompanion paper: Osterwalder–Schrader axioms for scalar QED$_3$ in the Coulomb phase. Project: https://github.com/marikgoldstein/scalar-qed-existenceCurrentNov 11, 2026