  The $L_p - E_p$ relation is a well-known relation in gamma-ray bursts. Its
implication remains unclear. We propose to investigate the underlying
mechanisms of this relation by considering the corresponding kinetic and
dynamic mechanisms separately. In this way, one can tell how much the kinetic
or dynamic mechanism contributes to the index of the relationship. Our analysis
gives rise to several conclusions. (1) The index of the kinetic effect in the
$L_p - E_p$ relation can simply be derived from the theory of special
relativity, which is generally larger than 2, depending on the situation
concerned. (2) The index of the dynamic effect in the relation can be deduced
from observation once a model of jets is adopted. According to current GRB
data, we find: the dynamic effect alone tends to make an anti-correlation
between $L_p$ and $E_p$; in terms of statistics, the dynamic effect is
obviously smaller than the kinetic effect; in the situation of jets with moving
discrete radio clouds which moves directly towards the observer, the index of
the dynamic effect is currently constrained within $(-1.6, -1)$, while in other
situations of jets, the constrains are different; both internal and external
shocks can account for the current data.
