Abstract
A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental (∼ Planck) length scale ℓ. We develop a general formalism based on wavelet decomposition of fields that takes this UV ‘opaqueness’ into account in a natural and mathematically well-defined manner. This is done by requiring fields in a local Lagrangian to be expandable in only the scaling parts of a (complete or, in a more general version, partial) wavelet Multi-Resolution Analysis. This delocalizes the interactions, now mediated through the opaque regions, inside which they are rapidly decaying. The opaque regions themselves are capable of discrete excitations of ∼ 1/ℓ spacing. The resulting effective Feynman rules, which give UV regulated and (perturbatively) unitary physical amplitudes, resemble those of string field theory.
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Tomboulis, E.T. Wavelet field decomposition and UV ‘opaqueness’. J. High Energ. Phys. 2021, 77 (2021). https://doi.org/10.1007/JHEP06(2021)077
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DOI: https://doi.org/10.1007/JHEP06(2021)077