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
17 - Counter-terms
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
The physicist’s counter-term method enriches the class of possible diagrams by adding new types of vertices. We explain in simple cases how this method can be used to re-parameterize a theory, and how the physicists use it to tame the diverging integrals by having “the counter terms cancel the divergences”. Assuming that the BPHZ method succeeds in producing finite results for the scattering amplitudes, we prove that the counter-term method succeeds too.
- Type
- Chapter
- Information
- What Is a Quantum Field Theory? , pp. 514 - 541Publisher: Cambridge University PressPrint publication year: 2022