Abstract
The formulation of the many-body problem by MARTIN and SCHWINGER is applied to a system of free electrons interacting with a phonon bath. Simplifying the general expression for the wave vector and frequency dependent complex conductivity to the case of a static dc situation the conductivity is expressed in terms of the LAPLACE transform of an appropriate GREEN'S function. By means of a simple diagram method a transport equation for this function is derived. In the lowest approximation the solution of this equation gives the BLOCH-GRÜNEISEN law for the conductivity of metals at low temperatures.
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