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This is a self-contained and hopefully readable account on the method ofcreation and annihilation operators (also known as the Fock spacerepresentation or the "second quantization" formalism) for non-relativisticquantum mechanics of many particles. Assuming knowledge only on conventionalquantum mechanics in the wave function formalism, we define the creation andannihilation operators, discuss their properties, and introduce correspondingrepresentations of states and operators of many-particle systems. As the titleof the note suggests, we cover most topics treated in sections 6.7 and 6.8 ofFeynman's "Statistical Mechanics: A Set of Lectures". As a preliminary, we alsocarefully discuss the symmetry of wave functions describing indistinguishableparticles.  We note that all the contents of the present note are completely standard,and the definitions and the derivations presented here have been known to many.Although the style of the present note may be slightly more mathematical thanstandard physics literatures, we do not try to achieve full mathematicalrigor.(Note to experts: In particular we here DERIVE the (anti)commutationrelations of the creation and annihilation operators, rather than simplydeclaring them. In this sense our approach is quite close to that of Feynman's.But we here focus on the action of creation/annihilation operators on general$N$ body wave functions, while Feynman makes a heavy use ofSlater-determinant-type states from the beginning. We hope that ourpresentation provides a better perspective on the formalism.)

Introduction to the "second quantization" formalism for non-relativistic  quantum mechanics: A possible substitution for Sections 6.7 and 6.8 of  Feynman's "Statistical Mechanics"