English

Quantum scalar field theories with fractional operators

High Energy Physics - Theory 2021-08-16 v3 General Relativity and Quantum Cosmology

Abstract

We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension. These theories are either ghost free or power-counting renormalizable but they cannot be both at the same time. However, some of them are one-loop unitary and finite, and possibly unitary and finite at all orders.

Keywords

Cite

@article{arxiv.2102.03363,
  title  = {Quantum scalar field theories with fractional operators},
  author = {Gianluca Calcagni},
  journal= {arXiv preprint arXiv:2102.03363},
  year   = {2021}
}

Comments

49 pages, 5 figures. v2: gravity part moved into a separate paper (arXiv:2106.15430), advanced/retarded Green's functions added, unitarity proof with self-interactions added, connection with IR nonlocal gravity models strengthened, references added; v3: minor typos corrected, mistake corrected in equation (119) which propagated to some equations but did not alter any of the conclusions

R2 v1 2026-06-23T22:53:10.502Z