Varying electric charge in multiscale spacetimes

Abstract

We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying-coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multifractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion.

15 pages. v2: minor typos corrected, references added

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• The minimally extended Varying Speed of Light (meVSL)
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• Cosmic microwave background and inflation in multi-fractional spacetimes
• ABC of multi-fractal spacetimes and fractional sea turtles
• Quantum field theory with varying couplings
• Standard Model in multiscale theories and observational constraints
• Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
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• Varying-Alpha and K-Essence
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
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• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Multifractional spacetimes from the Standard Model to cosmology