Chapter II.3 Proof of the Uniform BPH Theorem

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Acknowledgements ix
4. Part I. Introduction to Euclidean Field Theory
5. Chapter I.1 The Ultraviolet Problem 3
6. Chapter I.2 Euclidean Field Theory. The O.S. Axioms 15
7. Chapter I.3 The Φ⁴ Model 23
8. Chapter I.4 Feynman Graphs and Amplitudes 37
9. Chapter I.5 Borel Summability 54
10. Part II. Perturbative Renormalization
11. Chapter II.1 The Multiscale Representation and a Bound on Convergent Graphs 59
12. Chapter II.2 Renormalization Theory for Φ⁴₄ 74
13. Chapter II.3 Proof of the Uniform BPH Theorem 90
14. Chapter II.4 The Effective Expansion 111
15. Chapter II.5 Construction of “Wrong Sign” Planar Φ⁴₄ 123
16. Chapter II.6 The Large Order Behavior of Perturbation Theory 144
17. Part III. Constructive Renormalization
18. Chapter III.1 Single Scale Cluster and Mayer Expansions 171
19. Chapter III.2 The Phase Space Expansion: The Convergent Case 210
20. Chapter III.3 The Effective Expansion and Infrared Φ⁴₄ 241
21. Chapter III.4 The Gross-Neveu Model 272
22. Chapter III.5 The Ultraviolet Problem in Non-Abelian Gauge Theories 289
23. References and Bibliography 321
24. Index 333