  The general expression for the magnetoresistance (MR) due to the Lorentz
force is derived by using the Fermi liquid transport theory based on the Kubo
formula. The obtained gauge-invariant expression is exact for any strength of
the interaction, as for the most singular term with respect to 1/\gamma^\ast
(\gammak^\ast being the quasiparticle damping rate). By virtue of the
exactness, the conserving laws are satisfied rigorously in the present
expression, which is indispensable for avoiding unphysical solutions. Based on
the derived expression, we can calculate the MR within the framework of the
Baym-Kadanoff type conserving approximation, by including all the vertex
corrections required by the Ward identity. The present expression is
significant especially for strongly correlated systems because the current
vertex corrections will be much important. On the other hand, if we drop all
the vertex corrections in the formula, we get the MR of the relaxation time
approximation (RTA), which is commonly used because of the simplicity. However,
the RTA is dangerous because it may give unphysical results owing to the lack
of conserving laws. In conclusion, the present work enables us to study the MR
with satisfying the conserving laws which is highly demanded in strongly
correlated electrons, such as high-Tc superconductors, organic metals, and
heavy Fermion systems. In Appendix D, we reply to the comment by O. Narikiyo
[cond-mat/0006028]. (Note that Appendix D exists only in the e-preprint
version.)
