Quantum field theory 1: Basics in mathematics and physics

✍ Scribed by Zeidler, Eberhard

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 1045
• Category: Library

✦ Table of Contents

Content: Cover --
Contents --
Part I. Introduction --
Prologue --
1. Historical Introduction --
1.1 The Revolution of Physics --
1.2 Quantization in a Nutshell --
1.3 The Role of Gottingen --
1.4 The Gottingen Tragedy --
1.5 Highlights in the Sciences --
1.6 The Emergence of Physical Mathematics --
a New Dimension of Mathematics --
1.7 The Seven Millennium Prize Problems of the Clay Mathematics Institute --
2. Phenomenology of the Standard Model for Elementary Particles --
2.1 The System of Units --
2.2 Waves in Physics --
2.3 Historical Background --
2.4 The Standard Model in Particle Physics --
2.5 Magic Formulas --
2.6 Quantum Numbers of Elementary Particles --
2.7 The Fundamental Role of Symmetry in Physics --
2.8 Symmetry Breaking --
2.9 The Structure of Interactions in Nature --
3. The Challenge of Different Scales in Nature --
3.1 The Trouble with Scale Changes --
3.2 Wilson's Renormalization Group Theory in Physics --
3.3 Stable and Unstable Manifolds --
3.4 A Glance at Conformal Field Theories --
Part II. Basic Techniques in Mathematics --
4. Analyticity --
4.1 Power Series Expansion --
4.2 Deformation Invariance of Integrals --
4.3 Cauchy's Integral Formula --
4.4 Cauchy's Residue Formula and Topological Charges --
4.5 The Winding Number --
4.6 Gauss' Fundamental Theorem of Algebra --
4.7 Compactification of the Complex Plane --
4.8 Analytic Continuation and the Local-Global Principle --
4.9 Integrals and Riemann Surfaces --
4.10 Domains of Holomorphy --
4.11 A Glance at Analytic S-Matrix Theory --
4.12 Important Applications --
5. A Glance at Topology --
5.1 Local and Global Properties of the Universe --
5.2 Bolzano's Existence Principle --
5.3 Elementary Geometric Notions --
5.4 Manifolds and Diffeomorphisms --
5.5 Topological Spaces, Homeomorphisms, and Deformations --
5.6 Topological Quantum Numbers --
5.7 Quantum States --
5.8 Perspectives --
6. Many-Particle Systems in Mathematics and Physics --
6.1 Partition Function in Statistical Physics --
6.2 Euler's Partition Function --
6.3 Discrete Laplace Transformation --
6.4 Integral Transformations --
6.5 The Riemann Zeta Function --
6.6 The Casimir Effect in Quantum Field Theory and the Epstein Zeta Function --
6.7 Appendix: The Mellin Transformation and Other Useful Analytic Techniques by Don Zagier --
7. Rigorous Finite-Dimensional Magic Formulas of Quantum Field Theory --
7.1 Geometrization of Physics --
7.2 Ariadne's Thread in Quantum Field Theory --
7.3 Linear Spaces --
7.4 Finite-Dimensional Hilbert Spaces --
7.5 Groups --
7.6 Lie Algebras --
7.7 Lie's Logarithmic Trick for Matrix Groups --
7.8 Lie Groups --
7.9 Basic Notions in Quantum Physics --
7.10 Fourier Series --
7.11 Dirac Calculus in Finite-Dimensional Hilbert Spaces --
7.12 The Trace of a Linear Operator --
7.13 Banach Spaces --
7.14 Probability and Hilbert's Spectral Family of an Observable --
7.15 Transition Probabilities, S-Matrix, and Unitary Operators ...

✦ Subjects

Quantum field theory.;Kwantumveldentheorie.;Quantenfeldtheorie.;Champs, Théorie quantique des.