Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- PART I Basics
- Part II Spin
- Part III Interactions
- Part IV Renormalization
- Part V Complements
- Appendix A Complements on Representations
- Appendix B End of Proof of Stone’s Theorem
- Appendix C Canonical Commutation Relations
- Appendix D A Crash Course on Lie Algebras
- Appendix E Special Relativity
- Appendix F Does a Position Operator Exist?
- Appendix G More on the Representations of the Poincaré Group
- Appendix H Hamiltonian Formalism for Classical Fields
- Appendix I Quantization of the Electromagnetic Field through the Gupta–Bleuler Approach
- Appendix J Lippmann–Schwinger Equations and Scattering States
- Appendix K Functions on Surfaces and Distributions
- Appendix L What Is a Tempered Distribution Really?
- Appendix M Wightman Axioms and Haag’s Theorem
- Appendix N Feynman Propagator and Klein–Gordon Equation
- Appendix O Yukawa Potential
- Appendix P Principal Values and Delta Functions
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
Appendix C - Canonical Commutation Relations
from Part V - Complements
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
- Part V Complements
- Appendix A Complements on Representations
- Appendix B End of Proof of Stone’s Theorem
- Appendix C Canonical Commutation Relations
- Appendix D A Crash Course on Lie Algebras
- Appendix E Special Relativity
- Appendix F Does a Position Operator Exist?
- Appendix G More on the Representations of the Poincaré Group
- Appendix H Hamiltonian Formalism for Classical Fields
- Appendix I Quantization of the Electromagnetic Field through the Gupta–Bleuler Approach
- Appendix J Lippmann–Schwinger Equations and Scattering States
- Appendix K Functions on Surfaces and Distributions
- Appendix L What Is a Tempered Distribution Really?
- Appendix M Wightman Axioms and Haag’s Theorem
- Appendix N Feynman Propagator and Klein–Gordon Equation
- Appendix O Yukawa Potential
- Appendix P Principal Values and Delta Functions
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
Summary
We study the canonical commutation relation, and give a complete proof of a fundamental result of Stone and von Neumann: A finite set of operators satisfying (the proper form of) these relations is essentially unique. We also detail why this result miserably fails for infinite sets of operators.
- Type
- Chapter
- Information
- What Is a Quantum Field Theory? , pp. 616 - 634Publisher: Cambridge University PressPrint publication year: 2022