{
  "abstract": "This is the eighth paper of a programme constructing the Feynman functional integral without a Wick rotation, based on the non-absolutely convergent Henstock–Kurzweil (HK) integral and on Kuelbs–Steadman spaces. Here the bosonic sector of an abelian gauge theory — Maxwell theory — is constructed as a continuum HK integral on the four-torus T^4: with the oscillating cylindrical premeasure of the previous stage, an explicit spectral truncation |n_mu| <= N (dim V_N = 4(2N+1)^4), Landau gauge fixing, and the continuum limit N -> infinity understood as convergence in the Kuelbs–Steadman space KS_2. Machine-verified: the quadraticity and the gauge invariance of the continuum Maxwell action; the diagonalisation of the truncated action in the Fourier modes; the independence of the abelian Faddeev–Popov operator of the connection and the equality Delta_FP = 1 of the normalised determinant; the unique solvability of the Landau condition on every non-constant mode (the abelian case has no Gribov copies); the HK integrability of F e^{iS_M^{(N)}} on compact boxes; the closed form of the gauge-fixed Fresnel value Z_N = (2 pi i)^{M_N} prod_{0<|n|<=N} |2 pi n|^{-2}, M_N = (2N+1)^4 - 1, and its independence of the truncation scheme; the projective consistency of the normalised premeasure, the Cauchy property of the truncated integrals in KS_2 and the uniqueness of the limit; the nilpotency and the invariance of the abelian BRS transformation together with the Slavnov–Taylor identities. The scope is stated honestly: the zeta-regularised value Delta_M = exp(zeta'(0)) remains a paper-level statement; the interacting non-abelian theory is not constructed here, and the Gribov problem is not solved — the abelian case simply has no Gribov copies, and the present paper serves as a test case for the continuum-limit machinery. A deterministic numerical script confirms all eight checks. The paper also contains preparatory material for the non-abelian case: the explicit linear deformation of the Faddeev–Popov operator with the bound ||M_1^{(N,K)}(A)|| <= C||A|| and positive definiteness for small fields; the cut-out violation functional together with its elementary bound; and a precisely stated singular-direction conjecture, which remains a conjecture and is nowhere used as an established statement. An explicit summability criterion for the increments in KS_2 is added as well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Yu. N. Berdinsky",
      "orcid": "0009-0003-1858-004X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yhjqfx06b7ew.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23440893",
  "fulltext_url": null,
  "id": "5yhjqfx06b7ew",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23440893",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23440893/files/InfiniteHK8_en.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yhjqfx06b7ew.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:21:11Z",
      "native_id": "23440893",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23440893"
    }
  ],
  "subjects": [],
  "title": "Abelian Maxwell Theory as a Continuum Henstock-Kurzweil Integral: Gauge Invariance, Spectral Truncation, and Stability",
  "title_text": "Abelian Maxwell Theory as a Continuum Henstock-Kurzweil Integral: Gauge Invariance, Spectral Truncation, and Stability",
  "type": "preprint",
  "updated_at": "2026-10-31T12:21:11Z",
  "url": "https://research.draconitic.com/paper/5yhjqfx06b7ew",
  "venue": "Zenodo",
  "versions": []
}