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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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Infinite-dimensional analysis and quantum probability have undergone significant developments in the last few years and created many applications. This volume includes four expository articles on recent developments in quantum field theory, quantum stochastic differential equations, free probability and quantum white noise calculus, which are targeted also for graduate study. The fourteen research papers deal with most of the current topics, and their interconnections reflect a vivid development in interacting Fock space, infinite-dimensional groups, stochastic independence, non-commutative ce
Dimensional analysis --- Quantum theory --- Probabilities --- Quantum field theory --- Physical measurements
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Les applications à la physique statistique et à la physique quantique : les méthodes et concepts fondamentaux et des applications à la physique des phénomènes critiques et à celle des particules élémentaires.
Quantum field theory. --- Statistical mechanics. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics
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Geometry --- Group theory --- Lie algebras --- Mathematical physics --- Particles (Nuclear physics) --- Quantum field theory --- Mathematics
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Quantum field theory --- Quantum optics --- Nonlinear optics --- Mathematical physics --- Physique mathématique --- Mathematical models --- Physique mathématique --- Quantum field theory - Mathematical models --- Quantum optics - Mathematical models --- Nonlinear optics - Mathematical models
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This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.
Quantum field theory. --- Lattice theory. --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics)
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The concept of quarks and gluons is used as a basis for formulating quantum chromodynamics, which represents a theory of the strong interactions of hadrons. The theory of electroweak interaction generalizes Fermi's theory of beta decay and unifies the theories of weak and electromagnetic interactions. In this book the author presents the general methods of quantization of physical fields, including Bose, Fermi, and gauge fields, along with methods for eliminating divergences arising in the modern theory of interacting fields. Fields and Fundamental Interactions is an indispensable reference for those in quantum theory, quantum electrodynamics, and elementary particle physics.
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"This book deals with new applications for coupled map lattices in quantum field theories and elementary particle physics"--P. xiii.
Coupled map lattices. --- Quantum field theory. --- Stochastic processes. --- String models. --- Chaotic behavior in systems. --- Statistical mechanics. --- Particles (Nuclear physics)
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This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants o
Quantum field theory. --- Knot theory. --- Three-manifolds (Topology) --- Invariants. --- Mathematical physics. --- Physical mathematics --- Physics --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Knots (Topology) --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Mathematics --- Quantum field theory --- Knot theory --- Mathematical physics
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