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Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.

Fermi liquid theory --- Fermi surfaces --- Hartree-Fock approximation --- Many-body problem --- Quantum field theory --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Hartree approximation --- Hartree-Fock-Slater approximation --- Approximation theory --- Atoms --- Energy-band theory of solids --- Self-consistent field theory --- Surfaces, Fermi --- Electrons --- Free electron theory of metals --- Quantum statistics --- Landau Fermi liquid theory --- Landau theory of Fermi liquids --- Landau's theory of Fermi liquids --- Fermi liquids