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The general expression for the magnetoresistance (MR) due to the Lorentzforce is derived by using the Fermi liquid transport theory based on the Kuboformula. The obtained gauge-invariant expression is exact for any strength ofthe interaction, as for the most singular term with respect to 1/\gamma^\ast(\gammak^\ast being the quasiparticle damping rate). By virtue of theexactness, the conserving laws are satisfied rigorously in the presentexpression, which is indispensable for avoiding unphysical solutions. Based onthe derived expression, we can calculate the MR within the framework of theBaym-Kadanoff type conserving approximation, by including all the vertexcorrections required by the Ward identity. The present expression issignificant especially for strongly correlated systems because the currentvertex corrections will be much important. On the other hand, if we drop allthe vertex corrections in the formula, we get the MR of the relaxation timeapproximation (RTA), which is commonly used because of the simplicity. However,the RTA is dangerous because it may give unphysical results owing to the lackof conserving laws. In conclusion, the present work enables us to study the MRwith satisfying the conserving laws which is highly demanded in stronglycorrelated electrons, such as high-Tc superconductors, organic metals, andheavy 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-preprintversion.)Comment: 28 pages, 23 figure

General formula for the magnetoresistance on the basis of Fermi liquid theory