Operators and Representation Theory (eBook)

Palle E.T. Jorgensen (Autor)

eBook Download: EPUB

2017 | Third
304 Seiten
Dover Publications (Verlag)
978-0-486-82257-0 (ISBN)

Infos

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

---

Suitable for advanced undergraduates and graduate students in mathematics and physics, this three-part treatment of operators and representation theory begins with background material on definitions and terminology as well as on operators in Hilbert space. The introductory section concludes with a look at the imprimitivity theorem, which grounds in more mathematical language the work of Wigner on representations of the Poincaré and Galilei groups.The second part of the monograph addresses the algebras of operators in Hilbert space, broadening the mathematics used in earlier versions of quantum theory. There are many examples in which the Hamiltonian, the operator that translates a quantum system in time, can be written as a polynomial in elements of an underlying Lie algebra. This section deals with properties of such operators. Part 3 explores covariant representation and connections, with a particular focus on infinite-dimensional Lie algebras. Connections to mathematical physics are stressed throughout the text, which concludes with three helpful appendixes, including a Guide to the Literature.

Autor

Palle E. T. Jorgensen is Professor of Mathematics at the University of Iowa.

Inhalt

ForewordPreface to the 2017 Dover EditionPreface to the 2008 Dover EditionPreface to the Original EditionAcknowledgmentsNotationPart 1.Background Material1. Introduction and Overview2. Definitions and Terminology3. Operators in Hilbert Space4. The Imprimitivity TheoremPart 2. Algebras of Operators on Hilbert Space5. Domains of Representations6. Operators in the Enveloping Algebra7. Spectral TheoryPart 3. Covariant Representations and Connections8. Infinite-Dimensional Lie AlgebrasAppendix A. Integrability of Lie AlgebrasAppendix B. Ofter Cited AboveAppendix C. Guide to the LiteratureBibliographyIndex 

Produkt-Details

• Erscheint lt. Verlag: 22.5.2017
• Reihe/Serie: Dover Books on Physics
• Sprache: englisch
• Maße: 160 x 160 mm
• Gewicht: 449 g
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Schlagworte: Algebra • books about physics • Complex • covariant representation and connections • Galilei • hilbert space • imprimitivity theorem • Infinite-dimensional Lie algebras • Infinite dimensional Lie Algebras • Lie algebra • Math • Mathematical Physics • Mathematics • Non-fiction • Nonfiction • phenomenon, • Physics • Poincare • Poincaré • polynomials • quantum system in time • Quantum Theory • reference text • relativistic quantum physics • Science • science and math • symmetry • wigner
• ISBN-10: 0-486-82257-5 / 0486822575
• ISBN-13: 978-0-486-82257-0 / 9780486822570