Quantum and Statistical Field Theory [Paperback]

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As a fundamental branch of theoretical physics, quantum field theory has led, in the last 20 years, to spectacular progress in our understanding of phase transitions and elementary particles. This textbook emphasizes the underlying unity of the concepts and methods used in both domains, and

presents in clear language topics such as the perturbative expansion, Feynman diagrams, renormalization, and the renormalization group. It contains detailed applications of critical phenomena to condensed matter physics, such as the calculation of critical exponents and a discussion of the XY

model. Applications to particle physics include quantum electrodynamics and chromodynamics, electroweak interactions, and lattice gauge theories. The book is based on courses given over several years on statistical mechanics and field theory, and is written at graduate level. It attempts to

guide the reader through a somewhat difficult and sometimes intricate subject in as clear a manner as possible, leading to a level of understanding where more advanced textbooks and research articles will be accessible. The only textbook covering the subject at this level, the work is thus an ideal

guide for graduate and postgraduate students in physics, researchers in quantum and statistical field theory, and those from other fields of physics seeking an introduction to quantum field theory. A large number of problems are given to test the reader's grasp of the ideas.

Part I: Critical Phenomena; Introduction to critical phenomena; Landau theory; The Renormalization group; Two-dimensional models; Part II: Perturbation theory and renormalization: The Euclidean Scalar Field: The perturbation expansion and Feynman diagrams; Renormalization; The Callan-Symanzik equations; Part III: The Quantum Theory of Scalar Fields: Path integrals in quantum and in statistical mechanics; Quantization of the Klein-Gordon field; Green's functions and the S matrix; Part IV: Gauge Theories: Quantization of the Dirac Field and the Electromagnetic Field: Quantum electrodynamics; Non-Abelian gauge theories; Appendices; Index; References