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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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Antiferromagnetism --- Antiferromagnetisme --- Haute température [Superconductivité à ] --- High Tc superconductivity --- High critical temperature superconductivity --- High temperature superconductivity --- Hoge temperatuur superconductiviteit --- Hubbard model --- Modèle d'Hubbard --- Superconductiviteit [Hoge temperatuur ] --- Superconductivité à haute température --- Temperatuur superconductiviteit [Hoge ] --- Température [Superconductivité à haute ] --- antiferromagnétisme --- 538.94 --- 530.19 --- Model, Hubbard --- Energy-band theory of solids --- Superconductivity --- Ferromagnetism --- Quantum liquids and solids --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Antiferromagnetism. --- High temperature superconductivity. --- Hubbard model. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 538.94 Quantum liquids and solids --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc

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P-adic analysis. --- Mathematical physics --- 51-7 --- 530.19 --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- P-adic analysis --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Physical mathematics --- Physics --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc --- Mathematics

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String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. Here, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.--From publisher description.

Hyperspace --- String models --- Fourth dimension --- Fourth dimension. --- Hyperspace. --- String models. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- 530.19 --- 512.7 --- Space of more than three dimensions --- Time travel --- Models, String --- String theory --- Nuclear reactions --- Algebraic configurations in hyperspace --- Geometry, Differential --- Geometry, Non-Euclidean --- Space and time --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Algebraic geometry. Commutative rings and algebras --- Foundations --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 512.7 Algebraic geometry. Commutative rings and algebras --- Hyperespace --- Modèles des cordes vibrantes (Physique nucléaire) --- Quatrième dimension --- Modèles des cordes vibrantes (Physique nucléaire) --- Quatrième dimension --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc

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Quantum field theory. --- Statistical mechanics. --- Théorie quantique des champs --- Mécanique statistique --- Statistical physics --- Quantum mechanics. Quantumfield theory --- Quantum field theory --- 536.75 --- 530.19 --- Entropy. Statistical thermodynamics. Irreversible processes --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 536.75 Entropy. Statistical thermodynamics. Irreversible processes --- Statistical mechanics --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Thermodynamics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc