  For more than half a century, most of the plasma scientists have encountered
a violation of the conservation laws of charge, momentum, and energy whenever
they have numerically solve the first-principle equations of kinetic plasmas,
such as the relativistic Vlasov--Maxwell system. This fatal problem is brought
by the fact that both the Vlasov and Maxwell equations are indirectly
associated with the conservation laws by means of some mathematical
manipulations. Here we propose a quadratic conservative scheme, which can
strictly maintain the conservation laws by discretizing the relativistic
Vlasov--Maxwell system. A discrete product rule and summation-by-parts are the
key players in the construction of the quadratic conservative scheme. Numerical
experiments of the relativistic two-stream instability and relativistic Weibel
instability prove the validity of our computational theory, and the proposed
strategy will open the doors to the first-principle studies of mesoscopic and
macroscopic plasma physics.
