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Fractions and fakeons in quantum field theory

Damiano Anselmi*

  • *Contact author: damiano.anselmi@unipi.it
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Phys. Rev. D 114, 065009 – Published 9 September, 2026

DOI: https://doi.org/10.1103/75jy-gbbl

Abstract

We investigate formulations of quantum field theories whose kinetic terms involve fractional or continuous powers of the d’Alembert operator. The primary requirements are perturbative unitarity and a well-defined classical limit with a finite number of initial conditions. A direct approach consists of continuing the correlation functions from Euclidean space to Minkowski spacetime using the fakeon prescription for the fractional part of the power. Alternative formulations arise through decomposition, in which the fractional part is represented as a continuum of ordinary fakeons. These options are infinite in number and yield inequivalent Minkowskian theories with the same Euclidean counterpart. We demonstrate these features at tree level and for bubble diagrams. We also point out potential pitfalls in the calculations. Finally, we show how to treat continuous powers of covariant d’Alembertians in fractional gauge and gravity theories. The Ward and Cutkosky identities hold in all formulations.

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Phys. Rev. D 114, 065009– Published 9 September, 2026
  • Received 14 June 2026
  • Accepted 3 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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