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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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In life and work, Claudio Bunster (formerly Teitelboim) prefers extreme challenges. Bunster, a physicist who contemplates brain-warping theories of space and time, returned to his native Chile from the United States precisely when most intellectuals would have stayed clear— during the middle of the Pinochet dictatorship (K. Mossman, Proceedings of the National Academy of Sciences) Against this backdrop, Bunster founded the Centro de Estudios Científicos (CECS), a world class institute for frontier science research in Chile. His mentor, John A. Wheeler often used Teddy Roosevelt’s advice, "Do what you can, where you are, with what you have." "I followed his advice," said Bunster. "At latitude 40°S there is a science institute where one can find the footprints of Wheeler in every corner." As a true pioneer, Bunster was ahead of his time, opening roads, pushing the frontiers, under extreme conditions, in unexplored environments. Throughout his career, black holes, monopoles, the Antarctic vastness and the entire universe, have been the objects of his fascination: extreme, simple objects where beauty is best captured and displayed. On 10 and 11 January 2008, the meeting Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity –Claudio’s Fest took place in Valdivia to celebrate Claudio Bunster’s 60th birthday. This volume collects the contributions that were discussed at this meeting by many of Bunster’s colleagues and longtime collaborators. Articles by L. Brink, S. Carlip, F. Englert, S. Hawking, M. Henneaux, C.W. Misner and L. Susskind, among others, highlight the broad impact of Bunster, providing unique insightful views on many topics addressed by him in his scientific career, ranging from black holes and symmetries in gravity and supergravity, to cosmology. The meeting was co-organized by the CECS and the International Solvay Institutes.

Physics. --- Quantum theory. --- Teitelboim, Claudio. --- Quantum theory --- Physics --- Atomic Physics --- Physical Sciences & Mathematics --- Natural philosophy --- Philosophy, Natural --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Teitelboim Weitzmann, Claudio --- Weitzmann, Claudio Teitelboim --- Bunster, Claudio --- Gravitation. --- Quantum physics. --- Elementary particles (Physics). --- Quantum field theory. --- Elementary Particles, Quantum Field Theory. --- Quantum Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Physical sciences --- Dynamics --- Mechanics --- Thermodynamics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Relativistic quantum field theory --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Properties

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En suivant deux fils rouges, l’histoire des grandes révolutions de la physique au xxe siècle et l’abstraction progressive du concept de symétrie, de son usage ordinaire en géométrie à son application aux lois de la physique, cette leçon inaugurale aborde un des défis majeurs de la physique actuelle, celui de réconcilier la relativité d'Einstein et la mécanique quantique, théories amplement vérifiées empiriquement et pourtant incompatibles. C’est peut-être dans une symétrie immense, décrite en théorie des groupes par des groupes très particuliers, que réside la clé pour formuler cette théorie plus fondamentale de la gravitation, qui pourrait permettre la grande synthèse avec la mécanique quantique.

Multidisciplinary --- physique --- mécanique quantique --- relativité --- gravitation --- symétrie --- Big Bang --- théorie des cordes --- théorie des groupes --- Physics --- Gravity --- Quantum physics (quantum mechanics & quantum field theory) --- Relativity physics

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"The Cosmological Singularity written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski-Khalatnikov-Lifshitz (BKL) conjecture on this field"--

Singularities (Mathematics) --- Cosmology --- Space and time. --- Supergravity. --- Singularités (Mathématiques) --- Cosmologie --- Espace et temps --- Supergravité --- Mathematics. --- Mathématiques