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PreprintCC BY 4.0arXiv

On the Meaning of Localization in Non-Local Quantum Field Theory

  • E. J. Thompson
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Abstract

In this paper we explore and derive an uncertainty principle for an ultraviolet complete nonlocal quantum field theory where under our hypothesises of an induced equal time detector response kernel, we then prove that the observed localization width obeys an exact variance addition law. Then when we combine this with the ordinary Heisenberg inequality and we obtain a nonlocal uncertainty relation. The bound reduces to the usual local relation in the infrared or local limit when EM → ∞, while in the ultraviolet it implies a minimal localization length of order LM. We go on to explain what this means for locality, microcausality, the interpretation of spacetime points, and the ultraviolet structure of quantum field theory. In this formulation we note and prove that spacetime will remain a Lorentz covariant continuum at the level of the manifold description but pointlike localization ceases to be a physically realizable observable notion below the nonlocality scale.

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Cite

BibTeXRIS
BibTeX
@misc{thompson2026meaning,
  title = {{On the Meaning of Localization in Non-Local Quantum Field Theory}},
  author = {E. J. Thompson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.27387},
  eprint = {2606.27387},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.27387},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Meaning of Localization in Non-Local Quantum Field Theory
AU  - E. J. Thompson
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2606.27387
UR  - https://arxiv.org/abs/2606.27387
AB  - In this paper we explore and derive an uncertainty principle for an ultraviolet complete nonlocal quantum field theory where under our hypothesises of an induced equal time detector response kernel, we then prove that the observed localization width obeys an exact variance addition law. Then when we combine this with the ordinary Heisenberg inequality and we obtain a nonlocal uncertainty relation. The bound reduces to the usual local relation in the infrared or local limit when E_M → ∞, while in the ultraviolet it implies a minimal localization length of order L_M. We go on to explain what this means for locality, microcausality, the interpretation of spacetime points, and the ultraviolet structure of quantum field theory. In this formulation we note and prove that spacetime will remain a Lorentz covariant continuum at the level of the manifold description but pointlike localization ceases to be a physically realizable observable notion below the nonlocality scale.
ER  -