Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- PART I Basics
- Part II Spin
- Part III Interactions
- Part IV Renormalization
- 15 Prologue: Power Counting
- 16 The Bogoliubov–Parasiuk–Hepp–Zimmermann Scheme
- 17 Counter-terms
- 18 Controlling Singularities
- 19 Proof of Convergence of the BPHZ Scheme
- Part V Complements
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
16 - The Bogoliubov–Parasiuk–Hepp–Zimmermann Scheme
from Part IV - Renormalization
Published online by Cambridge University Press: 22 February 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- PART I Basics
- Part II Spin
- Part III Interactions
- Part IV Renormalization
- 15 Prologue: Power Counting
- 16 The Bogoliubov–Parasiuk–Hepp–Zimmermann Scheme
- 17 Counter-terms
- 18 Controlling Singularities
- 19 Proof of Convergence of the BPHZ Scheme
- Part V Complements
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
Summary
We describe the BPHZ scheme of renormalization. The diverging integrals are tamed by replacing the integrand by a regularized version of it with better properties. Historically the scheme was recursive, removing in turn the divergences from the small diagrams to the larger ones, but now the regularization of the integrand is directly given as a sum of terms by the forest formula. In the end, the scheme can be seen as a very clever use of Taylor’s formula.
- Type
- Chapter
- Information
- What Is a Quantum Field Theory? , pp. 496 - 513Publisher: Cambridge University PressPrint publication year: 2022