Theorem on the Magnetoconductivity of Metals

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Abstract
Under rather general assumptions it can be proved that the conductivity of a metal is monotonically nonincreasing with magnetic field. In the proof given it is assumed that the electron motion can be described by a fermion Boltzmann equation with arbitrary multiple band structure and an arbitrary law of scattering. However, the magnetic field is to enter only through the Lorentz force term. Exceptions to the theorem are known; they arise probably because the magnetic field influences the scattering process.

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