2015/12/31 by Gianluca Calcagni, Giuseppe Nardelli, David Rodríguez Fernández +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Electroweak interaction #Electroweak scale #Energy (signal processing) #Exponent #Integer (computer science) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Upper and lower bounds #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.94.045018
published as Phys. Rev. D 94, 045018 (2016) · 25 pages. v2: authors' metadata corrected; v3: references added, new material added including a comparison with varying-couplings and effective field theories, a section on predictivity and falsifiability of multiscale theories, a discussion on classical CPT, expanded conclusions, and new QED constraints from the fine-structure constant; v3: minor typos corrected to match the published version
arxiv created 2016/08/29 · openalex publication_date 2016/08/29 · arxiv updated 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) q-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale t*, \ensuremathℓ* and E*, we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound t*<10^\ensuremath-23 s. For the natural choice \ensuremathα0=1/2 of the fractional exponent in the measure, this bound is strengthened to t*<10^\ensuremath-29 s, corresponding to \ensuremathℓ*<10^\ensuremath-20 m and E*>28 TeV. Stronger bounds are obtained from the measurement of the fine-structure constant. (ii) In the theory with q-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds t*<10^\ensuremath-13 s and E*>35 MeV. For \ensuremathα0=1/2, the Lamb shift alone yields t*<10^\ensuremath-27 s, \ensuremathℓ*<10^\ensuremath-19 m and E*>450 GeV.