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PreprintCC BY 4.0arXiv

Scaling Limits as Extensions of Continuous Bundles of C*-algebras

  • Kade Cicchella
  • Benjamin H. Feintzeig
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Abstract

We analyze scaling limits in algebraic quantum field theory using continuous bundles of C*-algebras. Different conditions of continuity on such bundles encode different strengths of approximation of the theory by its scaling limit. As a proof of concept, we consider the small-distance scaling limit of the theory of a massive free scalar field, which corresponds to a massless free scalar field. We provide a number of examples of local algebras of observables for which the corresponding bundle of C*-algebras representing the scaling limit is merely lower semicontinuous. Further, we construct an algebra of nonlocal observables for which the corresponding bundle of C*-algebras representing the scaling limit is uniformly continuous.

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Cite

BibTeXRIS
BibTeX
@misc{cicchella2026scaling,
  title = {{Scaling Limits as Extensions of Continuous Bundles of C*-algebras}},
  author = {Kade Cicchella and Benjamin H. Feintzeig},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40924},
  eprint = {2610.40924},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40924},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Scaling Limits as Extensions of Continuous Bundles of C*-algebras
AU  - Kade Cicchella
AU  - Benjamin H. Feintzeig
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40924
UR  - https://arxiv.org/abs/2610.40924
AB  - We analyze scaling limits in algebraic quantum field theory using continuous bundles of C*-algebras. Different conditions of continuity on such bundles encode different strengths of approximation of the theory by its scaling limit. As a proof of concept, we consider the small-distance scaling limit of the theory of a massive free scalar field, which corresponds to a massless free scalar field. We provide a number of examples of local algebras of observables for which the corresponding bundle of C*-algebras representing the scaling limit is merely lower semicontinuous. Further, we construct an algebra of nonlocal observables for which the corresponding bundle of C*-algebras representing the scaling limit is uniformly continuous.
ER  -