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Quantum field theory (QFT) provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy. Many of these essays were first presented as papers at the conference "Ontological Aspects of Quantum Field Theory", held at the Zentrum für interdisziplinäre Forschung (ZiF), Bielefeld, Germany. The essays contain cutting-edge work
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The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.
Quantum field theory. --- Quantum field theory --- Research.
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Providing a new perspective on quantum field theory, this book gives a pedagogical exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research in theoretical physics. After describing non-perturbative methods in detail, it uses these methods to explore two-dimensional and four-dimensional gauge dynamics. The book concludes with a summary emphasizing the interplay between two- and four-dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics in particular, are thoroughly described. Published originally in 2010, this title has been reissued as an Open Access publication on Cambridge Core.
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This monograph presents recent developments in quantum field theory at finite temperature. By using Lie groups, ideas from thermal theory are considered with concepts of symmetry, allowing for applications not only to quantum field theory but also to transport theory, quantum optics and statistical mechanics. This includes an analysis of geometrical and topological aspects of spatially confined systems with applications to the Casimir effect, superconductivity and phase transitions. Finally, some developments in open systems are also considered. The book provides a unified picture of the funda
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Les idées du groupe de renormalisation développées pour la physique statistique dans les années 1970, en grande partie grâce au prix Nobel de physique Kenneth Wilson, ont entièrement renouvelé ce que l’on appelait la théorie relativiste des champs quantiques, née dans les années 1930 et développée sous la forme de l’électrodynamique quantique dans les années 1950. Un résultat de ce renouvellement est la théorie statistique des champs, une boîte à outils de tout physicien théoricien, de la physique des hautes énergies à la physique statistique. Ce livre, qui repose sur un enseignement de plusieurs années, notamment dans le parcours « Physique théorique » du Master 2 « Concepts fondamentaux de la physique », à l’École normale supérieure, est une introduction pédagogique à cet ensemble incontournable de notions. Il est destiné aux étudiants et aux chercheurs. La théorie statistique des champs repose sur la profonde analogie entre les fluctuations quantiques d’un système quantique en dimension d’espace D et les fluctuations thermiques d’un système classique en équilibre à une température absolue T dans un espace de dimension (D + 1), la constante de Planck h jouant le rôle de la température T. Ce premier tome développe l’aspect « quantique » de la théorie. La première partie du livre est consacrée à l’intégrale de chemin, qui permet de mettre en évidence d’une façon particulièrement claire cette correspondance entre les deux types de fluctuations, sans négliger des aspects avancés (bosons et fermions, états cohérents, spin). Dans une deuxième partie, l’auteur utilise l’exemple typique de la théorie en φ4 pour un exposé détaillé de l’intégrale fonctionnelle, du développement perturbatif, des graphes de Feynman, de la renormalisation perturbative et du groupe de renormalisation en théorie des champs. Le deuxième tome sera consacré aux applications du groupe de renormalisation à la physique statistique, en particulier le calcul des exposants critiques. Seront aussi abordés des sujets reliés : modèle XY, polymères, chaînes de spin, mouillage et membranes, ainsi qu’une introduction à l’invariance conforme et à l’invariance d’échelle en taille finie.
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Michael Kachelriess introduces quantum field theory together with its most important applications to cosmology and astroparticle physics. Applications such as topological defects, phase transitions, dark matter, external gravitational fields and black holes help students to bridge the gap between undergraduate courses and research literature.
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Providing a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity, this text reviews loop representation theory, Maxwell theory, Yang-Mills theories, lattice techniques, knot and braid theory, and describes applications in quantum gravity. A final chapter considers future prospects.
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Everything around us is made of 'stuff', from planets, to books, to our own bodies. Whatever it is, we call it matter or material substance. It is solid; it has mass. But what is matter, exactly? We are taught in school that matter is not continuous, but discrete. As a few of the philosophers of ancient Greece once speculated, nearly two and a half thousand years ago, matter comes in 'lumps', and science has relentlessly peeled away successive layers of matter to reveal its ultimate constituents. "Albert Einstein once claimed that without belief in the inner harmony of our world, there could be no science. But modern science has revealed that the inner harmony of some of the simplest phenomena can be startlingly beautiful in its complexity. This is certainly true of matter, and its most commonplace property, mass. We have come a long way since the conjectures of the Greek atomists. We know for sure that atoms exist, and we also know that they're divisible. They consist of electrons, orbiting nuclei of protons and neutrons. We know that protons and neutrons are in turn composed of quarks. And we have found that elementary particles inside atoms behave like waves: mysterious phantoms of probability. We have identified several families of subatomic particles, and now recognize that 'empty' space fizzes with virtual particles. we think now of mass in terms of the energies of interactions. Elementary particles gain mass by interacting with the Higgs field, revealed by the discovery of the Higgs boson, but we still don't understand why some particles interact more strongly than others. As Jim Baggott explains in this absorbing account that takes us from atoms to quarks, gluons, and quantum chromodynamics, we have journeyed far, but we have yet to fully understand the fundamental nature of mass."--
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One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.
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