Introduction to the theory of many-body systems (Q2762919)

The book is a collection of lecture notes of an introductory course on the theory of many body systems. It begins with an introduction to the formulation of second quantization for fermions and makes a first acquaintance with some properties of interacting electron fluid, in particular, Fermi gas and liquid, liquid \(He^3\), plasma oscillation and Wigner crystallization. The next section on single-particle Green's function, is on the investigation of its general properties introducing the concept of quasi-particles and a precise definition of self-energy. This is followed by a section on the Landau theory of normal Fermi-liquid including its thermodynamic properties, collective excitation of \(He^3\) liquid and plasma. The next section on the two-particle Green's function describes the interaction between the quasi-particles and the collective excitations of the many-body systems. It includes as special cases the linear density response function of the fluid, density fluctuation and its dissipation. The section on the perturbative expansion is on the treatment of Green's function by perturbative expansion and Feynman diagrams. The emphasis is on the techniques and exact results, with illustration on the Hartree-Fock self-energy and dielectric screening in the so-called random phase approximation. In the following section on dielectric screening in quantum plasma (author's field of contribution), the main properties of state and dynamic screening are reviewed at various levels of approximation. The section on electron-phonon interaction in simple metals, is basically an important application of the theory. It ends with a brief discussion of strong scattering of conduction electrons by isolated impurities in simple metals. The pen-ultimate section on magnetism of conduction electron is concerned with some aspects of the behaviour of conduction electron in an applied magnetic field, in particular, the paramagnetic spin response and the transition to the ferromagnetic state. The last section on the superconductivity in metals gives an introduction to `conventional' superconductivity in metals, with main emphasis on Bardeen-Cooper-Schrieff theory and related developments. It is supplemented with two important appendices, (i) Luttinger liquid in \(D=1\) and (ii) Linear response theory for free electrons in \(D\)-dimension.NEWLINENEWLINENEWLINEThe book is being reprinted (1997), with minor changes and updating from the first edition (1994). Notwithstanding the informal style of presentation as lecture notes, the reviewer also concurs with the author's expectation that ``The booklet will help advanced students to catch the flavour of the subject and to get a feeling for the type of physical questions that one should ask in theory and experiment with regard to the macroscopic systems of interacting particles''.