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Noncommutative Geometry, Quantum Fields and Motives
This entry collects material related to the book
on noncommutative geometry, quantum field theory and motives in physics.
Contents
Chapter 1. Quantum fields, noncommutative spaces, and motives
1. Introduction
2. Basics of perturbative QFT
3. Feynman diagrams
4. Dimensional regularization
5. The graph by graph method of Bogoliubov-Parasiuk-Hepp-Zimmermann
6. The Connes-Kreimer theory of perturbative renormalization
7. Renormalization and the Riemann-Hilbert correspondence
8. Motives in a nutshell
9. The Standard model of elementary particle physics
10. The framework of (metric) noncommutative geometry
11. The spectral action principle
12. Noncommutative geometry and the Standard Model
13. The finite noncommutative geometry
14. The product geometry
15. Bosons as inner fluctuations
16. The spectral action and the Standard Model Lagrangian
17. The Standard Model Lagrangian from the spectral action
18. Functional integral
19. Dimensional regularization and noncommutative geometry
Chapter 2. The Riemann zeta function and noncommutative geometry
1. Introduction
2. Counting primes and zeta function
3. Classical and quantum mechancis of zeta
Chapter 3. Quantum statistical mechanics and Galois symmetries
Last revised on November 8, 2013 at 10:45:13.
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