Constraining the Lorentz invariance violation from the continuous
  spectra of short gamma-ray bursts
  In quantum gravity, a foamy structure of space-time leads to Lorentz
invariance violation (LIV). As the most energetic astrophysical processes in
the Universe, gamma-ray bursts (GRBs) provide an effective way to probe quantum
gravity effects. We use continuous spectra of 20 short GRBs detected by the
Swift satellite to give a conservative lower limit of quantum gravity energy
scale $M_\textrm{QG} $. Due to the LIV effect, photons with different energy
have different velocities. This will lead to the delayed arrival of high energy
photons relative to the low energy ones. Based on the fact that the LIV-induced
time delay can't be longer than the duration of a GRB, we present the most
conservative estimation of the quantum gravity energy scales from 20 short
GRBs. The most strict constraint, $M_\textrm{QG}>5.05\times10^{14}$ GeV, is
from GRB 140622A.
