  It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of
the electron self-energy function $ \Sigma (k, \varepsilon + i0) \equiv
\Sigma^{R}(k, \varepsilon) $ are, $ {\rm Im} \Sigma^{R} (k, \varepsilon) =
-a\varepsilon^{2}|\varepsilon - \xi_{k}|^{- \gamma (k)} $ where $a$ is some
constant, $\xi_{k} = \varepsilon(k)-\mu, \varepsilon(k)$ being the band energy,
and the critical exponent $ \gamma(k) $, which depends on the curvature of the
Fermi surface at $ k $, satisfies, $ 0 \leq \gamma(k) \leq 1 $. This leads to a
new type of electron liquid, which is the Fermi liquid in the limit of $
\varepsilon, \xi_{k} \rightarrow 0 $ but for $ \xi_{k} \neq 0 $ has a split
one-particle spectra as in the Tomonaga-Luttinger liquid.
