  We compile 23 Gamma-ray Bursts (GRBs) and 21 blazars with estimated Doppler
factors, and the Doppler factors of GRBs are estimated from their Lorentz
factors by assuming their jet viewing angles \theta->0 degree. Using the
conventional assumption that the prompt emission of GRBs is dominated by the
synchrotron radiation, we calculate the synchrotron luminosity of GRBs from
their total isotropic energy and burst duration. Intriguingly, we discover a
uniform correlation between the synchrotron luminosity and Doppler factor,
L_syn \propto D^3.1, for GRBs and blazars, which suggests that they may share
some similar jet physics. One possible reason is that GRBs and blazars have,
more or less, similar intrinsic synchrotron luminosities and both of them are
strongly enhanced by the beaming effect. After Doppler and redshift-correction,
we find that the intrinsic peak energy of the GRBs ranges from 0.1 to 3 keV
with a typical value of 1 keV. We further correct the beaming effect for the
observed luminosity of GRBs and find that there exists a positive correlation
between the intrinsic synchrotron luminosity and peak energy for GRBs, which is
similar to that of blazars. Our results suggest that both the intrinsic
positive correlation and the beaming effect may be responsible for the observed
tight correlation between the isotropic energy and the peak energy in GRBs (so
called "Amati" relation).
