  This is the first of two lectures on a new powerful technique employed by
Brown, Preston, and Singleton (BPS) to calculate transport quantities in a
plasma. This exposition will be self-contained and intended for those who are
not specialists in quantum field theory, where the technique of dimensional
continuation exploited by BPS first arose. The method is highlighted by the
interesting analogy between the Coulomb logarithm of Lyman Spitzer on the one
hand, and the Lamb shift as calculated by Hans Bethe on the other. BPS employed
the method in a novel way that provides the leading and subleading behavior for
processes with competing disparate length or energy scales. They calculated the
temperature equilibration rate to leading and next-to-leading order in the
plasma number density for any two species in a plasma that are in thermal
equilibrium with themselves, but not necessarily with each other. A special
case of this calculation is the electron-ion temperature equilibration rate. It
should be emphasized that the BPS result is not a model, but rather it is an
exact calculation of the leading terms in a well-defined perturbation theory.
This exact result differs from approximations and models given in the
literature.
