  Using the Hugenholtz-Van Hove theorem, we derive analytical expressions for
the nuclear symmetry energy $E_{sym}(\rho)$ and its density slope $L(\rho)$ in
terms of the Lorentz covariant nucleon self-energies in isospin asymmetric
nuclear matter. These general expressions are useful for determining the
density dependence of the symmetry energy and understanding the Lorentz
structure and the microscopic origin of the nuclear symmetry energy in
relativistic covariant formulism. As an example, we analyze the Lorentz
covariant nucleon self-energy decomposition of $E_{sym}(\rho)$ and $L(\rho)$
and derive the corresponding analytical expressions within the nonlinear
$\sigma$-$\omega$-$\rho$-$\delta$ relativistic mean field model.
