  We suggest a new method of calculations for a clean Fermi gas with a
repulsion in any dimension. This method is based on writing equations for
quasiclassical Green functions and reducing them to equations for collective
spin and charge excitations. The spin excitations interact with each other and
this leads to non-trivial physics. Writing the solution of the equations and
the partition function in terms of a functional integral over supervectors and
averaging over fluctuating fields we come to an effective field theory
describing the spin excitations. In some respects, the theory is similar to
bosonization but also includes the ``ghost'' excitations which prevents
overcounting of the degrees of freedom. Expansion in the interaction reveals
logarithmic in temperature corrections. This enables us to suggest a
renormalization group scheme and derive renormalization group equations.
Solving these equations and using their solutions for calculating thermodynamic
quantities we obtain explicit expression for the specific heat containing only
an effective amplitude of the backward scattering. This amplitude has a
complicated dependence on the logarithm of temperature, which leads to a
non-trivial temperature dependence of the specific heat.
