  Using mean field approach, we provide analytical and numerical solution of
the symmetric Anderson lattice for arbitrary dimension at half filling. The
symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it
possible to study the behavior of an electron liquid in the Kondo lattice. We
have shown that, due to hybridization (through an effective field due to
localized electrons) of electrons with different spins and momenta $\textbf{k}$
and $\textbf{k}+\overrightarrow{\pi}$, the gap in the electron spectrum opens
at half filling. Such hybridization breaks the conservation of the total
magnetic momentum of electrons, the spontaneous symmetry is broken. The state
of electron liquid is characterized by a large Fermi surface. A gap in the
spectrum is calculated depending on the magnitude of the on-site Coulomb
repulsion and value of s-d hybridization for the chain, as well as for square
and cubic lattices. Anomalous behavior of the heat capacity at low temperatures
in the gapped state, which is realized in the symmetric Anderson lattice, was
also found.
