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This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail.The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

Gauge fields (Physics) --- Quantum theory --- Champs de jauge (Physique) --- Théorie quantique --- 530.19 --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Quantum theory. --- Gauge fields (Physics). --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Théorie quantique --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc

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« An Introduction to Quantum Field Theory » is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Feynman diagrams --- Gauge fields (Physics) --- Quantum field theory --- Renormalization (Physics) --- 530.19 --- 530.145 --- 530.145 Quantum theory --- Quantum theory --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Charge and mass renormalization --- Mass and charge renormalization --- Electric charge and distribution --- Mass (Physics) --- Physical measurements --- Relativistic quantum field theory --- Field theory (Physics) --- Relativity (Physics) --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Group theory --- Symmetry (Physics) --- Many-body problem --- Matrices --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc --- Quantum mechanics. Quantumfield theory --- Feynman diagrams. --- Gauge fields (Physics). --- Quantum field theory. --- Renormalization (Physics). --- Feynman, Diagrammes de --- Champs de jauge (Physique) --- Théorie quantique des champs --- Renormalisation (Physique) --- Théorie quantique des champs --- Renormalisation (physique) --- Champs de jauge (physique) --- Théorie quantique des champs. --- Feynman, Diagrammes de.