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The book is an introduction to quantum field theory and renormalization group. It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory.

Quantum field theory. --- Critical phenomena (Physics) --- Renormalization (Physics) --- Théorie quantique des champs --- Phénomène critique (Physique) --- Renormalisation (Physique) --- Quantum field theory --- 530 --- Charge and mass renormalization --- Mass and charge renormalization --- Electric charge and distribution --- Mass (Physics) --- Physical measurements --- Phenomena, Critical (Physics) --- Physics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Critical phenomena (Physics). --- Renormalization (Physics). --- Théorie quantique des champs --- Phénomène critique (Physique)

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The goal of this book is to introduce students to path integrals within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.

Path integrals. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Integrals, Path --- Integrals --- Probabilities --- Quantum theory --- Statistical physics

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Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work.The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.

Mathematical physics --- Field theory (Physics) --- Quantum field theory --- Renormalization (Physics) --- Charge and mass renormalization --- Mass and charge renormalization --- Electric charge and distribution --- Mass (Physics) --- Physical measurements --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Physical mathematics --- Mathematics --- Mathematical physics. --- Quantum field theory. --- Random matrices. --- Physique mathématique --- Champs, Théorie des (physique) --- Théorie quantique des champs --- Renormalisation (physique) --- Matrices aléatoires

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Path integrals --- Quantum theory --- Statistical physics

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Acqui 2006