In the 1992 edition of his book A Guide to Feynman Diagrams in the

Many-Body Problem, physicist Richard Mattuck compares the dilemma to trying to describe a galloping horse and all the grains of dust that it kicks up.

study the solution to the Kohn-Sham equation in the density functional theory of the quantum

many-body problem in the context of the electronic structure of the smoothly deformed macroscopic crystals.

With these tools in hand, the nonlinear

many-body problem, the molecular dynamics, the low dimensionality and nanostructures are then explored.

It seems that a truly rigorous and elegant solution will be achieved only by finding a mathematical transformation that reduces the

many-body problem to a one-body problem.

Among the topics are the validity of random matrix theories for many-particle systems, the angular-momentum dependence of the density of states, group theory and the propagation of operator averages, electromagnetic sum rules by spectral distribution methods, compound-nuclear tests of time reversal invariance in the nucleon-nucleon interaction, strength functions and spreading widths of simple shell model configurations, and underlying symmetries of realistic interactions and the nuclear

many-body problem.

Objective: The derivation of macroscopic (effective) equations from microscopic considerations is a long-standing challenge of the mathematical analysis of

many-body problems.

The rest of the book covers new elements of resonance theory, waves in periodic structures, wave mechanics on lattices, systems of coupled Schrodinger equations, and multidimensional and

many-body problems.