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Many-body problems and quantum field theory. An introduction. Transl. from the French by Steven Goldfarb. (English) Zbl 0986.81002

Texts and Monographs in Physics. Berlin: Springer. xiii, 441 p. (2002).
This text is a translation of a book originally published in French attempting to provide a very broad level of knowledge for graduate and Ph.D. students with different orientations, be it in condensed matter, nuclear matter or particle physics. Thus, the conception of the book is determined by pedagogy rather than completeness. The prerequisites are introductory courses to classical physics and quantum mechanics. While in Chapter 1 the authors recapitulate classical fields and some of their associated particles, i.e. photons and phonons, Chapter 2 already aims at the collective effects owing to Bose and Fermi statistics. The concepts of Fock space and second quantization are introduced in Chapter 3. Chapters 4, 5, and 6 are devoted to the use of the variational methods with a wide range of applications. Special emphasis is given to the idea of fermionic pairing occurring in both the BCS theory of superconductivity and nuclear matter.
In Chapter 8 the authors study the free quantized electromagnetic and scalar fields as model systems in order to provide the ground for a more general theory of relativistic quantized fields. It is here, where one misses some essential topics: the role of the Lorentz group or \(\text{SL}(2,\mathbb{C})\), Wigner’s characterization of particles by their masses and spins, the concept of spinor fields and the Dirac equation, non-Abelian gauge theories and the standard model, the path integral approach to quantized interacting fields, non-zero temperature states and their Green functions etc. Instead the authors jump ahead and explain the use of Feynman graphs with few applications (Compton scattering, radiative corrections, and electron-phonon interactions) stressing the existence of a common language for condensed matter and particle theory. The hope is expressed that the reader will discover the unity of thinking among different domains of physics.

MSC:

81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81V70 Many-body theory; quantum Hall effect
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