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This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization for constrained physical systems and its corresponding de Rham cohomology group structure. These were studied by theoretical physicists from the early 1960s and appeared in attempts to quantize rigorously some physical theories such as solitons and other models subject to geometrical constraints. In particular, phenomenological soliton theories such as Skyrmion and chiral bag models have seen a revival following experimental data from the SAMPLE and HAPPEX Collaborations, and these are discussed. The book describes how these model predictions were shown to include rigorous treatments of geometrical constraints because these constraints affect the predictions themselves. The application of the BRST symmetry to the de Rham cohomology contributes to a deep understanding of Hilbert space of constrained physical theories. Aimed at graduate-level students in quantum field theory, the book will also serve as a useful reference for those working in the field. An extensive bibliography guides the reader towards the source literature on particular topics.

Physics. --- Quantum Field Theories, String Theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Mathematical Methods in Physics. --- Nuclear Physics, Heavy Ions, Hadrons. --- Mathematical physics. --- Nuclear physics. --- Quantum theory. --- Physique --- Physique mathématique --- Physique nucléaire --- Théorie quantique --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Symmetry (Physics) --- Gauge fields (Physics) --- Homology theory. --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Cohomology theory --- Contrahomology theory --- Quantum field theory. --- String theory. --- Heavy ions. --- Hadrons. --- Elementary particles (Physics). --- Algebraic topology --- Field theory (Physics) --- Group theory --- Conservation laws (Physics) --- Physical mathematics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Mathematics --- Ions --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics)

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This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becchi-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. This extended new edition offers a multifaced insight into phenomenology of particles such as baryons and photons, in terms of extended objects. In particular, in the second edition, the baryons are described in hypersphere soliton model, and the photon properties are additionally included in stringy photon model and in Dirac type relativistic quantum mechanics for a photon. It offers a critical overview of the research in this area and unifies the existing literatures, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization and its de Rham cohomology group which contribute to a deep understanding of constrained physical theories. The book describes how solitons and other models subject to constraints include rigorous treatments of the geometrical constraints which affect the predictions themselves. The book is intended for use by any graduate-level student with quantum field and relativity theories, and it also serves as a useful reference for those working in the field. An extensive bibliography guides the reader toward the source literature on particular topics.

Elementary particles (Physics). --- Quantum field theory. --- Mathematical physics. --- Nuclear physics. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Mathematical Methods in Physics. --- Nuclear Physics.

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Mathematical physics --- Quantum mechanics. Quantumfield theory --- Elementary particles --- Nuclear physics --- elementaire deeltjes --- kwantumleer --- wiskunde --- fysica --- atoomfysica