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Quantum Field Theory III: Gauge Theory

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Cover of 'Quantum Field Theory III: Gauge Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Prologue
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    Chapter 2 The Euclidean Space E 3 (Hilbert Space and Lie Algebra Structure)
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    Chapter 3 Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)
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    Chapter 4 Representations of Symmetries in Mathematics and Physics, and Elementary Particles
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    Chapter 5 The Euclidean Manifold \(\mathbb{E}^{3}\)
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    Chapter 6 The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry
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    Chapter 7 Infinitesimal Rotations and Constraints in Physics
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    Chapter 8 Rotations, Quaternions, the Universal Covering Group, and the Electron Spin
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    Chapter 9 Changing Observers – A Glance at Invariant Theory Based on the Principle of the Correct Index Picture
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    Chapter 10 Applications of Invariant Theory to the Rotation Group
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    Chapter 11 Temperature Fields on the Euclidean Manifold \(\mathbb{E}^{3}\)
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    Chapter 12 Velocity Vector Fields on the Euclidean Manifold \(\mathbb{E}^{3}\)
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    Chapter 13 Covector Fields and Cartan’s Exterior Differential – the Beauty of Differential Forms
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    Chapter 14 The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field
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    Chapter 15 Symmetry Breaking
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    Chapter 16 The Noncommutative Yang–Mills SU(N)-Gauge Theory
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    Chapter 17 Cocycles and Observers
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    Chapter 18 The Axiomatic Geometric Approach to Bundles
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    Chapter 19 Inertial Systems and Einstein’s Principle of Special Relativity
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    Chapter 20 The Relativistic Invariance of the Maxwell Equations
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    Chapter 21 The Relativistic Invariance of the Dirac Equation and the Electron Spin
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    Chapter 22 The Language of Exact Sequences
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    Chapter 23 Electrical Circuits as a Paradigm in Homology and Cohomology
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    Chapter 24 The Electromagnetic Field and the de Rham Cohomology
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