Electrical conductivity of metals is usually discussed in undergraduate general physics textbooks [1 to 3] and also in introductory solid state physics textbooks (see for instance C. Kittel [4]). One of the achievements of these treatments is the “deduction” of the Paul Drude ‘s formula for the electrical conductivity of metals, which is stated as a function of the number of charge carriers per unit of volume, the quantum of elementary electric charge, the mass of the charge carriers, and the averaged time between collisions. However looking at the nicely famous textbook:”The Feynman Lectures on Physics”, I do not found any mention to the Drude formula for the electrical conductivity.

Unfortunately it is not possible to ask Feynman himself why this topic is missing in his outstanding book. May be he does not found (from his point of view) any satisfactory elementary explanation of this subject, or even to be not worth to talk about it in the text.

I would like to get the opinion of my colleagues about this fact.

References

[1] D. Halliday, R. Resnick, Fundamentals of Physics, 3d edition, Wiley, 1988.

[2] S. Borowitz, A. Beiser, Essentials of Physics, Addison-Wesley, 1966.

[3] Alaor Chaves, Física Básica - Eletromagnetismo (Editora LAB, Rio de Janeiro, 2007), cap. 10.

[4] C. Kittel, Introduction to Solid State Physics, 5th edition , Wiley, 1976 - Ch. 6

Just a note on the Drude's model:

This model has many set backs, and failed to explain several phenomena which were later explained by use of the quantum theory of solids. Semiclassical treatment was also successful in resolving some of the difficulties associated with Drude's theory. For example, the determination of the conductivity requires knowledge of the relaxation time (mean free time between collisions). This relaxation time was found to be temperature dependent, and no where in the free electron model was this dependence discussed. Further, the theory assumes that the resistivity arises from collisions with the heavy ions, which suggests that the meal free path should be of the order of inter-atomic spacings. However, orders of magnitude larger mean free paths were observed experimentally. Also, the use of the kinetic theory (in the free electron model) to determine the average velocity of the electron is certainly not correct; an order of magnitude larger velocities were reported. The sign and magnitude of the Hall coefficient also could not be explained by the classical theory of Drude. A semiclassical interpretation, at least, is required to resolve this anomalous behavior. The magnetoresistance also could not be explaind by Drude's theory. Even with the conductivity calculations,  Drude originally made a mistake and obtained a value which is half the correct value; this led him (erroneously) to obtain a value for the Lorentz number (in Wiedemann-Franz Law) in excellent agreement with experiment.

I would not use the free electron model!

Just another note:

the Drude Model had to fail for metal conductivity, since it is classical and electrons are not. It still works fine for the case of electrolytes and colloidal suspensions!

see e.g. Medebach et al J. Chem. Phys. 123, 104903 (2005).

Drude type conductivity in charged sphere colloidal crystals: density and temperature dependence

Ashcroft & Mermin in their first chapters give an excellent exposition on merits and problems of Drude & Co.

As soon as you decide to drop that idea for good, you're in to solid state physics, crystals, k-space etc until you comme back to the point where you have a representation of what a current carrynig state may look like. Its not whithin the scope of Feynman's books... (not explicitely, at least)

To summarize glibly, the Drude model works (or almost works) more or less by accident, like some other classical derivations that happen to give the same answers as the correct quantum mechanical versions.  This is unsurprising in the macroscopic realm, where we know why QM reduces to classical mechanics in the limit of the large, but it surprises us when we see it in the realm of the small, where QM rules.  We like our incompatibilities to be absolute.  Too bad. 

As to why Feynman omitted a patently incorrect derivation that accidentally gives approximately the right answer, ... do you really have to ask?

I have posted that same question in another forum of debates and I’ve got the following answer by Zhi Cheng: “I think Feynman is a prudent man. Perhaps there were some thing that he could not make sure in QED, he do not want to explore the metals’ electric conductivity prematurely.”

I received from my friend and colleague Nilton Penha Silva a private comment, something like this: “Zhi Cheng is on the right path!”

Indeed, a great dream of the condensed matter’s theorist would be, starting from a very fundamental theory as Quantum Electrodynamics, to evaluate the transport properties of conductors and superconductors (both of BCS-kind and also the high-TC ones). However, as far as I know, this broad subject has not been achieved yet.

Feynman tried to solve the problem of superconductivity and failed. He remarked that "superconductivity is one thing that I never understood". I guess he was very much set back at this failure and was unwilling to discuss this topic. He knew much of the theory of metallic conductivity is wrong not to talk about superconductivity.