2011

Quantum Field Theory III: Gauge Theory

A Bridge between Mathematicians and Physicists

Authors:

ISBN: 978-3-642-22420-1 (Print) 978-3-642-22421-8 (Online)

Table of contents (24 chapters)

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  1. Front Matter

    Pages I-XXXII

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    Book Chapter

    Pages 1-67

    Prologue

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    Book Chapter

    Pages 69-114

    The Euclidean Space E 3 (Hilbert Space and Lie Algebra Structure)

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    Book Chapter

    Pages 115-179

    Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)

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    Book Chapter

    Pages 181-320

    Representations of Symmetries in Mathematics and Physics, and Elementary Particles

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    Book Chapter

    Pages 321-354

    The Euclidean Manifold \(\mathbb{E}^{3}\)

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    Book Chapter

    Pages 355-370

    The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry

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    Book Chapter

    Pages 371-423

    Infinitesimal Rotations and Constraints in Physics

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    Book Chapter

    Pages 425-437

    Rotations, Quaternions, the Universal Covering Group, and the Electron Spin

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    Book Chapter

    Pages 439-556

    Changing Observers – A Glance at Invariant Theory Based on the Principle of the Correct Index Picture

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    Book Chapter

    Pages 557-643

    Applications of Invariant Theory to the Rotation Group

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    Book Chapter

    Pages 645-658

    Temperature Fields on the Euclidean Manifold \(\mathbb{E}^{3}\)

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    Book Chapter

    Pages 659-664

    Velocity Vector Fields on the Euclidean Manifold \(\mathbb{E}^{3}\)

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    Book Chapter

    Pages 665-809

    Covector Fields and Cartan’s Exterior Differential – the Beauty of Differential Forms

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    Book Chapter

    Pages 811-830

    The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field

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    Book Chapter

    Pages 831-841

    Symmetry Breaking

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    Book Chapter

    Pages 843-870

    The Noncommutative Yang–Mills SU(N)-Gauge Theory

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    Book Chapter

    Pages 871-873

    Cocycles and Observers

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    Book Chapter

    Pages 875-903

    The Axiomatic Geometric Approach to Bundles

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    Book Chapter

    Pages 905-934

    Inertial Systems and Einstein’s Principle of Special Relativity

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    Book Chapter

    Pages 935-993

    The Relativistic Invariance of the Maxwell Equations

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