Wavelet field decomposition and UV ‘opaqueness’

• Main Author: E. T. Tomboulis
• Format: Article
• Language: English
• Published: SpringerOpen 2021-06-01
• Series: Journal of High Energy Physics
• Subjects: Effective Field Theories; Scattering Amplitudes
• Online Access: https://doi.org/10.1007/JHEP06(2021)077

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.