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 A - Complements on Representations
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 answer some natural mathematical questions concerning representations. We develop the theory of induced representations for finite groups, which sheds considerable light on the structure of the induced representation of the Poincaré group studied in Chapter 8.
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- What Is a Quantum Field Theory? , pp. 593 - 611Publisher: Cambridge University PressPrint publication year: 2022