Noncommutative Geometry, Quantum Fields and Motives

This entry collects material related to the book

on noncommutative geometry, quantum field theory and motives in physics.


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

Chapter 4. Endomotives, thermodynamics, and the Weil explicit formula

category: reference

Revised on November 8, 2013 10:45:13 by Urs Schreiber (