space. Usually $up$ and $down$ quarks are assumed as degenerated in mass.

The NJL model is generally solved after applying the well known bosonization procedure following Eguchi \[\] to arrive at the model expressed in terms of physically observed particles’ fields $\sigma({\vec x}), {\vec\pi}({\vec x})$:

$${\cal L}_{NJL}' = \bar q \  [ \ i \gamma^{\mu}\partial_{\mu} -
g (\sigma + i\, {\vec\pi \vec\tau}\, \gamma_5 )\ ] \, q -
{1\over 2} \mu^2 (\sigma^2 + {\vec\pi}^2) +
(m_0\, \mu^2 / g) \, \sigma
\ . \eqno(\NEWLAG)$$

The new coupling constant $\mu^2$ is related to the initial $G$ by: $G=g^2/\mu^2$. Here, $g$ is the physical pion–quark coupling constant implying that $\vec\pi$ are the physical pion fields. The meson fields are constrained to the chiral circle to reproduce the pion decay constant:

$$\sigma^2({\vec x}) + {\vec\pi}^2({\vec x}) = f^2_{\pi}
\ , \eqno(\CHIRCIR)$$

where $f_{\pi}=93~MeV$ is the pion decay constant.

In fact, an equivalent effective chiral quark meson theory \[,\] can be derived from the instanton model of the QCD vacuum.

In the chiral quark soliton model \[-\] based on the lagrangean () (frequently reffered simply as NJL model) the baryons appear as a bound state of $N_c$ valence quarks coupled to the polarized Dirac 