  We consider the singular electron-electron interaction corrections to the
transport coefficients in disordered metals to test the validity of the
Wiedemann-Franz law. We develop a local, quantum kinetic equation approach in
which the charge and energy conservation laws are explicitly obeyed. To obtain
the local description, we introduce bosonic distribution functions for the
neutral, low-energy collective modes (electron-hole pairs). The resulting
system of kinetic equations enables us to distinguish between the different
physical processes involved in the charge and energy transport: elastic
electron scattering affects both, while the inelastic processes influence only
the latter. Moreover, the neutral bosons, though incapable of transporting
charge, contribute significantly to the energy transport. In our approach we
calculate on equal footing the electrical and thermal conductivities and the
specific heat in any dimension. We found that the Wiedemann-Franz law is always
violated by the interaction corrections; the violation is larger for one- and
two-dimensional systems in the diffusive regime $T\tau \ll \hbar$ and it is due
to the energy transported by the neutral bosons. For two-dimensional systems in
the quasi-ballistic regime $T\tau \gg \hbar$ the inelastic scattering of the
electron on the bosons also contributes to the violation.
