Operators and representation theory : canonical models for algebras of operators arising in quantum mechanics /
| Main Author: | |
|---|---|
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Mineola, New York :
Dover Publications,
2017.
|
| Edition: | Third edition. |
| Series: | Dover books on physics.
|
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Foreword by Professor William Klink, the University of Iowa Physics Department; Foreword; Preface to the Dover Editions; The 2015 Dover Ed.; Preface to the Original Edition; Acknowledgements; Notation; Part 1. Background Material; Chapter 1. Introduction and Overview; Chapter 2. Definitions and Terminology; 2.1. Notation; 2.2. Brackets; 2.3. Representations; 2.4. Units; 2.5. Projective Representations; 2.6. Central Extensions; 2.7. Modules; 2.8. Norm and Unboundedness; 2.9. C*-norms; 2.10. Groups, Algebras, and Operators; Chapter 3. Operators in Hilbert Space; 3.1. Domain and Graph
- 3.2. The Adjoint Operator3.3. Selfadjoint Operators; 3.4. The Operator T*T; 3.5. The Polar Decomposition; 3.6. Normal Operators; 3.7. Functional Calculus; 3.8. Real and Imaginary Parts; 3.9. Positive Operators; Chapter 4. The Imprimitivity Theorem; 4.1. Integration and Unitary Equivalence; 4.2. Applications; Part 2. Algebras of Operators on Hilbert Space; Chapter 5. Domains of Representations; 5.1. Introduction; 5.2. Selfadjoint Representations; 5.3. The Derived Representation; 5.4. Integrability of Selfadjoint Representations; 5.5. Scalar Casimir Operator: A Special Case
- Chapter 6. Operators in the Enveloping Algebra6.1. Central Elements; 6.2. Second Order Elements; 6.3. The Element x+iy; 6.4. Higher Order Elements; Chapter 7. Spectral Theory; 7.0. Survey of Results; 7.1. Discrete Spectrum; 7.2. Trace Formula: High Energy Behavior; 7.3. Continuous Spectrum; 7.4. Lebesgue Spectrum; Part 3. Covariant Representations and Connections; Chapter 8. Infinite-Dimensional Lie Algebras; 8.1. Rotation Algebras; 8.2. Completions of AC(L); 8.3. Extensions of ""0362 by U(A(R)); 8.4. Extensions and u(n,1); 8.5. Vector Fields on the Circle; 8.6. Noncommutative Tori
- Appendix A. Integrability of Lie AlgebrasAppendix B. Often cited above; Appendix C. Guide to the Literature; Bibliography; Index