Non-local hyperdifferential momentum operators in quantum field theory free from tachyons: the case of neutral mesons

An extended non-local field equations characterised by modified dispersion relations have been constructed based on non-local differential and hyperdifferential quantum operators. The dispersion relations obtained are found to be comparable to those obtained within the framework of unified theories and the covariant Kempf–Mangano algebra but free from tachyons. For the case of neutral meson, the upper limit of the characteristic length scale was found to be very close to the nuclear radius obtained from the study of \(\beta ^{+} \) ${\beta }^{+}$ -decay energy from finite-sized nuclei.