Quantum field theory. [Vol.] III, Gauge theory : a bridge between mathematicians and physicists

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the __classical aspects__ of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles.This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle __force equals curvature:__ Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. __Quantum Field Theory__ builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). Front Matter....Pages I-XXXII Prologue....Pages 1-67 The Euclidean Space E 3 (Hilbert Space and Lie Algebra Structure)....Pages 69-114 Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)....Pages 115-179 Representations of Symmetries in Mathematics and Physics, and Elementary Particles....Pages 181-320 The Euclidean Manifold $\mathbb{E}^{3}$ ....Pages 321-354 The Lie Group U (1) as a Paradigm in Harmonic Analysis and Geometry....Pages 355-370 Infinitesimal Rotations and Constraints in Physics....Pages 371-423 Rotations, Quaternions, the Universal Covering Group, and the Electron Spin....Pages 425-437 Changing Observers – A Glance at Invariant Theory Based on the Principle of the Correct Index Picture....Pages 439-556 Applications of Invariant Theory to the Rotation Group....Pages 557-643 Temperature Fields on the Euclidean Manifold $\mathbb{E}^{3}$ ....Pages 645-658 Velocity Vector Fields on the Euclidean Manifold $\mathbb{E}^{3}$ ....Pages 659-664 Covector Fields and Cartan’s Exterior Differential – the Beauty of Differential Forms....Pages 665-809 The Commutative Weyl U (1)-Gauge Theory and the Electromagnetic Field....Pages 811-830 Symmetry Breaking....Pages 831-841 The Noncommutative Yang–Mills SU ( N )-Gauge Theory....Pages 843-870 Cocycles and Observers....Pages 871-873 The Axiomatic Geometric Approach to Bundles....Pages 875-903 Inertial Systems and Einstein’s Principle of Special Relativity....Pages 905-934 The Relativistic Invariance of the Maxwell Equations....Pages 935-993 The Relativistic Invariance of the Dirac Equation and the Electron Spin....Pages 995-1002 The Language of Exact Sequences....Pages 1003-1008 Electrical Circuits as a Paradigm in Homology and Cohomology....Pages 1009-1026 The Electromagnetic Field and the de Rham Cohomology....Pages 1027-1067 Back Matter....Pages 1069-1126 In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction).--Publisher description of v.1 This is the third volume of a modern introduction [ projected 6 volumes ] to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. This book seeks to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to discover interesting interrelationships between quite diverse mathematical topics. For students of physics fairly advanced mathematics, beyond that included in the usual curriculum in physics, is presented