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Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman's ideas. This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathem

Feynman integrals. --- Feynman diagrams.

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This author provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. His aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions of renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience a final appendix provides a discussion of the metric used, and an easy-to-use dictionary connecting equations written with different metrics. Written as a textbook, many diagrams, exercises and examples are included. This book will be used by beginning graduate students taking courses in particle physics or quantum field theory, as well as by researchers as a source and reference book on Feynman diagrams and rules.

Feynman diagrams. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Many-body problem --- Matrices --- Quantum theory --- Feynman diagrams

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"The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon. The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics"--

Gauge fields (Physics) --- Particles (Nuclear physics) --- Weak interactions (Nuclear physics) --- Quantum electrodynamics. --- Feynman diagrams. --- SCIENCE / Nuclear Physics. --- SCIENCE / Physics. --- SCIENCE / Quantum Theory.

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The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Calculus' characterizes the most powerful methods in a systematic way. It concentrates on the methods that have been employed recently for most sophisticated calculations and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. It also shows how to choose adequate methods and combine them in a non-trivial way. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated.

Calculus, Integral --- Feynman integrals --- Feynman diagrams --- Multiple integrals --- Integral calculus --- Differential equations --- Quantum theory. --- Global analysis (Mathematics). --- Elementary Particles, Quantum Field Theory. --- Analysis. --- Quantum Physics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Feynman integrals. --- Elementary particles (Physics). --- Quantum field theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Quantum physics. --- 517.1 Mathematical analysis --- Mathematical analysis --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics

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Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Feynman integrals. --- Feynman, Intégrales de --- Feynman integrals --- Calculus --- Mathematical Theory --- Atomic Physics --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Functional analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Integral equations. --- Measure theory. --- Operator theory. --- Probabilities. --- Integral Equations. --- Measure and Integration. --- Functional Analysis. --- Operator Theory. --- Probability Theory and Stochastic Processes. --- Global Analysis and Analysis on Manifolds. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Functional analysis --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Equations, Integral --- Functional equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional calculus --- Calculus of variations --- Integral equations --- Math --- Science --- Feynman diagrams --- Multiple integrals --- Distribution (Probability theory. --- Global analysis. --- Global analysis (Mathematics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities